1
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Abraham GR, Chaderjian AS, N Nguyen AB, Wilken S, Saleh OA. Nucleic acid liquids. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:066601. [PMID: 38697088 DOI: 10.1088/1361-6633/ad4662] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Accepted: 05/02/2024] [Indexed: 05/04/2024]
Abstract
The confluence of recent discoveries of the roles of biomolecular liquids in living systems and modern abilities to precisely synthesize and modify nucleic acids (NAs) has led to a surge of interest in liquid phases of NAs. These phases can be formed primarily from NAs, as driven by base-pairing interactions, or from the electrostatic combination (coacervation) of negatively charged NAs and positively charged molecules. Generally, the use of sequence-engineered NAs provides the means to tune microsopic particle properties, and thus imbue specific, customizable behaviors into the resulting liquids. In this way, researchers have used NA liquids to tackle fundamental problems in the physics of finite valence soft materials, and to create liquids with novel structured and/or multi-functional properties. Here, we review this growing field, discussing the theoretical background of NA liquid phase separation, quantitative understanding of liquid material properties, and the broad and growing array of functional demonstrations in these materials. We close with a few comments discussing remaining open questions and challenges in the field.
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Affiliation(s)
- Gabrielle R Abraham
- Physics Department,University of California, Santa Barbara, CA 93106, United States of America
| | - Aria S Chaderjian
- Physics Department,University of California, Santa Barbara, CA 93106, United States of America
| | - Anna B N Nguyen
- Biomolecular Science and Engineering Program, University of California, Santa Barbara, CA 93106, United States of America
| | - Sam Wilken
- Physics Department,University of California, Santa Barbara, CA 93106, United States of America
- Materials Department, University of California, Santa Barbara, CA 93106, United States of America
| | - Omar A Saleh
- Physics Department,University of California, Santa Barbara, CA 93106, United States of America
- Biomolecular Science and Engineering Program, University of California, Santa Barbara, CA 93106, United States of America
- Materials Department, University of California, Santa Barbara, CA 93106, United States of America
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2
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Akritidis M, Fytas NG, Weigel M. Geometric clusters in the overlap of the Ising model. Phys Rev E 2023; 108:044145. [PMID: 37978672 DOI: 10.1103/physreve.108.044145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 09/22/2023] [Indexed: 11/19/2023]
Abstract
We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two distinct types of clusters in the overlap, which we dub soft- and hard-constraint clusters, and which are subsets of the regions of constant spin overlap. By means of Monte Carlo simulations and a finite-size scaling analysis we estimate the transition temperature as well as the set of critical exponents characterizing the percolation transitions undergone by these two cluster types. The results suggest that both soft- and hard-constraint clusters percolate at the critical temperature of the Ising model and their critical behavior is governed by the correlation-length exponent ν=1 found by Onsager. At the same time, they exhibit nonstandard and distinct sets of exponents for the average cluster size and percolation strength.
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Affiliation(s)
- Michail Akritidis
- Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 5FB, United Kingdom
| | - Nikolaos G Fytas
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
- Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, United Kingdom
| | - Martin Weigel
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
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3
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Klein W, Gould H, Matin S. Cluster scaling and critical points: A cautionary tale. Phys Rev E 2023; 108:034119. [PMID: 37849133 DOI: 10.1103/physreve.108.034119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 07/21/2023] [Indexed: 10/19/2023]
Abstract
Many systems in nature are conjectured to exist at a critical point, including the brain and earthquake faults. The primary reason for this conjecture is that the distribution of clusters (avalanches of firing neurons in the brain or regions of slip in earthquake faults) can be described by a power law. Because there are other mechanisms such as 1/f noise that can produce power laws, other criteria that the cluster critical exponents must satisfy can be used to conclude whether or not the observed power-law behavior indicates an underlying critical point rather than an alternate mechanism. We show how a possible misinterpretation of the cluster scaling data can lead one to incorrectly conclude that the measured critical exponents do not satisfy these criteria. Examples of the possible misinterpretation of the data for one-dimensional random site percolation and the one-dimensional Ising model are presented. We stress that the interpretation of a power-law cluster distribution indicating the presence of a critical point is subtle and its misinterpretation might lead to the abandonment of a promising area of research.
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Affiliation(s)
- W Klein
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Center for Computational Science, Boston University, Boston, Massachusetts 02215, USA
| | - Harvey Gould
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
| | - Sakib Matin
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA; Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, USA; and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, USA
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4
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Münster L, Weigel M. Cluster percolation in the two-dimensional Ising spin glass. Phys Rev E 2023; 107:054103. [PMID: 37329020 DOI: 10.1103/physreve.107.054103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2023] [Accepted: 03/03/2023] [Indexed: 06/18/2023]
Abstract
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a connection has not been fully established, and the numerical evidence remains incomplete. Here we use Monte Carlo simulations to study the percolation properties of several classes of clusters occurring in the Edwards-Anderson Ising spin-glass model in two dimensions. The Fortuin-Kasteleyn-Coniglio-Klein clusters originally defined for the ferromagnetic problem do percolate at a temperature that remains nonzero in the thermodynamic limit. On the Nishimori line, this location is accurately predicted by an argument due to Yamaguchi. More relevant for the spin-glass transition are clusters defined on the basis of the overlap of several replicas. We show that various such cluster types have percolation thresholds that shift to lower temperatures by increasing the system size, in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is linked to the difference in density of the two largest clusters, thus supporting a picture where the spin-glass transition corresponds to an emergent density difference of the two largest clusters inside the percolating phase.
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Affiliation(s)
- L Münster
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
| | - M Weigel
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
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5
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Zhang J, Zhang B, Xu J, Zhang W, Deng Y. Machine learning for percolation utilizing auxiliary Ising variables. Phys Rev E 2022; 105:024144. [PMID: 35291183 DOI: 10.1103/physreve.105.024144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for the machine learning study of the standard percolation as well as a variety of statistical mechanical systems in correlated percolation representation. We demonstrate that unsupervised machine learning is able to accurately locate the percolation threshold, independent of the spatial dimension of system or the type of phase transition, which can be first-order or continuous. Moreover, we show that, by neural network machine learning, auxiliary Ising configurations for different universalities can be classified with a high confidence level. Our results indicate that the auxiliary Ising mapping method, despite its simplicity, can advance the application of machine learning in statistical and condensed-matter physics.
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Affiliation(s)
- Junyin Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Bo Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Junyi Xu
- College of Physics and Optoelectronics, Taiyuan University of Technology, Shanxi 030024, China
| | - Wanzhou Zhang
- College of Physics and Optoelectronics, Taiyuan University of Technology, Shanxi 030024, China
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Youjin Deng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China
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6
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Abstract
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin–Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems.
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7
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Gagliardi G, Macheda F. Spinodal-assisted nucleation in the two-dimensional q-state Potts model with short-to-long-range interactions. Phys Rev E 2021; 104:014115. [PMID: 34412242 DOI: 10.1103/physreve.104.014115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Accepted: 06/07/2021] [Indexed: 11/07/2022]
Abstract
We study homogeneous nucleation in the two-dimensional q-state Potts model for q=3,5,10,20 and ferromagnetic couplings J_{ij}∝Θ(R-|i-j|) by means of Monte Carlo simulations employing heat bath dynamics. Metastability is induced in the low-temperature phase through an instantaneous quench of the magnetic field coupled to one of the q spin states. The quench depth is adjusted, depending on the value of temperature T, interaction range R, and number of states q, in such a way that a constant nucleation time is always obtained. In this setup, we analyze the crossover between the classical compact droplet regime occurring in the presence of short-range interactions R∼1 and the long-range regime R≫1 where the properties of nucleation are influenced by the presence of a mean-field spinodal singularity. We evaluate the metastable susceptibility of the order parameter as well as various critical droplet properties, which along with the evolution of the quench depth as a function of q,T and R are then compared with the field theoretical predictions valid in the large R limit to find the onset of spinodal-assisted nucleation. We find that, with a mild dependence of the values of q and T considered, spinodal scaling holds for interaction ranges R≳8-10 and that signatures of the presence of a pseudospinodal are already visible for remarkably small interaction ranges R∼4-5. The influence of spinodal singularities on the occurrence of multistep nucleation is also discussed.
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Affiliation(s)
- G Gagliardi
- Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy
| | - F Macheda
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom.,Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
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8
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Charbonneau P, Tarzia M. Solution of disordered microphases in the Bethe approximation. J Chem Phys 2021; 155:024501. [PMID: 34266261 DOI: 10.1063/5.0052111] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.
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Affiliation(s)
| | - Marco Tarzia
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
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9
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Zheng M, Charbonneau P. Characterization and efficient Monte Carlo sampling of disordered microphases. J Chem Phys 2021; 154:244506. [DOI: 10.1063/5.0052114] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Affiliation(s)
- Mingyuan Zheng
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
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10
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Rundle JB, Stein S, Donnellan A, Turcotte DL, Klein W, Saylor C. Reports on progress in physics the complex dynamics of earthquake fault systems: new approaches to forecasting and nowcasting of earthquakes. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:076801. [PMID: 33857928 DOI: 10.1088/1361-6633/abf893] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Accepted: 04/15/2021] [Indexed: 06/12/2023]
Abstract
Charles Richter's observation that 'only fools and charlatans predict earthquakes,' reflects the fact that despite more than 100 years of effort, seismologists remain unable to do so with reliable and accurate results. Meaningful prediction involves specifying the location, time, and size of an earthquake before it occurs to greater precision than expected purely by chance from the known statistics of earthquakes in an area. In this context, 'forecasting' implies a prediction with a specification of a probability of the time, location, and magnitude. Two general approaches have been used. In one, the rate of motion accumulating across faults and the amount of slip in past earthquakes is used to infer where and when future earthquakes will occur and the shaking that would be expected. Because the intervals between earthquakes are highly variable, these long-term forecasts are accurate to no better than a hundred years. They are thus valuable for earthquake hazard mitigation, given the long lives of structures, but have clear limitations. The second approach is to identify potentially observable changes in the Earth that precede earthquakes. Various precursors have been suggested, and may have been real in certain cases, but none have yet proved to be a general feature preceding all earthquakes or to stand out convincingly from the normal variability of the Earth's behavior. However, new types of data, models, and computational power may provide avenues for progress using machine learning that were not previously available. At present, it is unclear whether deterministic earthquake prediction is possible. The frustrations of this search have led to the observation that (echoing Yogi Berra) 'it is difficult to predict earthquakes, especially before they happen.' However, because success would be of enormous societal benefit, the search for methods of earthquake prediction and forecasting will likely continue. In this review, we note that the focus is on anticipating the earthquake rupture before it occurs, rather than characterizing it rapidly just after it occurs. The latter is the domain of earthquake early warning, which we do not treat in detail here, although we include a short discussion in the machine learning section at the end.
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Affiliation(s)
- John B Rundle
- Department of Physics and Astronomy, University of California, Davis, CA 95616, United States of America
- Department of Earth & Planetary Sciences, University of California, Davis, CA 95616, United States of America
- Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, United States of America
| | - Seth Stein
- Department of Earth and Planetary Sciences and Institute for Policy Research, Northwestern University, Evanston, IL 60208, United States of America
| | - Andrea Donnellan
- Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, United States of America
| | - Donald L Turcotte
- Department of Earth & Planetary Sciences, University of California, Davis, CA 95616, United States of America
| | - William Klein
- Department of Physics, Boston University, Boston, MA 02215, United States of America
| | - Cameron Saylor
- Department of Physics and Astronomy, University of California, Davis, CA 95616, United States of America
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11
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Huang S, Klein W, Gould H. Predicting nucleation using machine learning in the Ising model. Phys Rev E 2021; 103:033305. [PMID: 33862789 DOI: 10.1103/physreve.103.033305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Accepted: 01/16/2021] [Indexed: 11/07/2022]
Abstract
We use a convolutional neural network (CNN) and two logistic regression models to predict the probability of nucleation in the two-dimensional Ising model. The three methods successfully predict the probability for the nearest-neighbor Ising model for which classical nucleation is observed. The CNN outperforms the logistic regression models near the spinodal of the long-range Ising model, but the accuracy of its predictions decreases as the quenches approach the spinodal. An occlusion analysis suggests that this decrease is due to the vanishing difference between the density of the nucleating droplet and the background. Our results are consistent with the general conclusion that predictability decreases near a critical point.
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Affiliation(s)
- Shan Huang
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - William Klein
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Center for Computational Science, Boston University, Boston, Massachusetts 02215, USA
| | - Harvey Gould
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
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12
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Fierro A, Coniglio A, Zannetti M. Relation between statics and dynamics in the quench of the Ising model to below the critical point. Phys Rev E 2020; 102:012144. [PMID: 32794899 DOI: 10.1103/physreve.102.012144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Accepted: 06/16/2020] [Indexed: 11/07/2022]
Abstract
The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to ensure ergodicity breaking in the low-temperature phase. With this arrangement the infinite system is known to remain permanently out of equilibrium, i.e., there exists a well-defined asymptotic state which is time invariant but different from the ordered ferromagnetic state. In this paper we establish the critical nature of this invariant state by demonstrating numerically that the quench dynamics with periodic and antiperiodic boundary conditions are indistinguishable from each other. However, while the asymptotic state does not coincide with the equilibrium state for the periodic case, it coincides instead with the equilibrium state of the antiperiodic case, which in fact is critical. The specific example of the Ising model is shown to be one instance of a more general phenomenon, since an analogous picture emerges in the spherical model, where boundary conditions are kept fixed to periodic, while the breaking or preserving of ergodicity is managed by imposing the spherical constraint either sharply or smoothly.
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Affiliation(s)
- Annalisa Fierro
- CNR-SPIN, c/o Complesso di Monte S. Angelo, I-80126 Napoli, Italy
| | - Antonio Coniglio
- CNR-SPIN, c/o Complesso di Monte S. Angelo, I-80126 Napoli, Italy.,Physics Department, Università degli Studi di Napoli "Federico II", I-80126 Napoli, Italy
| | - Marco Zannetti
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, I-84084 Fisciano (SA), Italy
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13
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Timonin PN. Statistics of geometric clusters in Potts model: statistical mechanics approach. Proc Math Phys Eng Sci 2020; 476:20200215. [DOI: 10.1098/rspa.2020.0215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 07/20/2020] [Indexed: 11/12/2022] Open
Abstract
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters' size distributions is developed. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number
z
. The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.
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Affiliation(s)
- P. N. Timonin
- Southern Federal University, 344090 Rostov-on-Don, Stachki ave. 194, Russia
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14
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Fajen H, Hartmann AK, Young AP. Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model. Phys Rev E 2020; 102:012131. [PMID: 32795066 DOI: 10.1103/physreve.102.012131] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Accepted: 06/24/2020] [Indexed: 06/11/2023]
Abstract
We apply generalizations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional ±1 random-bond Ising model. The behavior of the model is determined by the temperature T and the concentration p of negative (antiferromagnetic) bonds. The ground state is ferromagnetic for 0≤p<p_{c}, and a spin glass for p_{c}<p≤0.5 where p_{c}≃0.222. We investigate the percolation transition of the Fortuin-Kasteleyn clusters as a function of temperature for large system sizes up to N=200^{3} spins. Except for p=0 the Fortuin-Kasteleyn percolation transition occurs at a higher temperature than the magnetic ordering temperature. This was known before for p=1/2 but here we provide evidence for a difference in transition temperatures even for p arbitrarily small. Furthermore, for all values of p>0, our data suggest that the percolation transition is universal, irrespective of whether the ground state exhibits ferromagnetic or spin-glass order, and is in the universality class of standard percolation. This shows that correlations in the bond occupancy of the Fortuin-Kasteleyn clusters are irrelevant, except for p=0 where the clusters are strictly tied to Ising correlations so the percolation transition is in the Ising universality class.
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Affiliation(s)
- Hauke Fajen
- Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
| | | | - A P Young
- Physics Department, University of California Santa Cruz, Santa Cruz, California 95064, USA
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15
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Pun CK, Matin S, Klein W, Gould H. Prediction in a driven-dissipative system displaying a continuous phase transition using machine learning. Phys Rev E 2020; 101:022102. [PMID: 32168593 DOI: 10.1103/physreve.101.022102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Accepted: 12/27/2019] [Indexed: 11/07/2022]
Abstract
Prediction in complex systems at criticality is believed to be very difficult, if not impossible. Of particular interest is whether earthquakes, whose distribution follows a power-law (Gutenberg-Richter) distribution, are in principle unpredictable. We study the predictability of event sizes in the Olmai-Feder-Christensen model at different proximities to criticality using a convolutional neural network. The distribution of event sizes satisfies a power law with a cutoff for large events. We find that predictability decreases as criticality is approached and that prediction is possible only for large, nonscaling events. Our results suggest that earthquake faults that satisfy Gutenberg-Richter scaling are difficult to forecast.
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Affiliation(s)
- Chon-Kit Pun
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Sakib Matin
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - W Klein
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA.,Center for Computational Science, Boston University, Boston, Massachusetts 02215, USA
| | - Harvey Gould
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA.,Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
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16
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Matin S, Pun CK, Gould H, Klein W. Effective ergodicity breaking phase transition in a driven-dissipative system. Phys Rev E 2020; 101:022103. [PMID: 32168561 DOI: 10.1103/physreve.101.022103] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Accepted: 01/02/2020] [Indexed: 11/07/2022]
Abstract
We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the system is effectively ergodic because the time-averaged stress on each site converges to the global spatial average. In contrast, below the critical noise, the stress on individual sites becomes trapped in different limit cycles, and the system is not ergodic. To characterize this transition, we use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. The order parameter is identified as the recurrence rate averaged over all sites and exhibits a jump at the critical noise. We also use ideas from percolation theory and analyze the clusters of failed sites to find numerical evidence that the transition, when approached from above, can be characterized by exponents that are consistent with hyperscaling.
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Affiliation(s)
- Sakib Matin
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Chon-Kit Pun
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Harvey Gould
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA.,Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
| | - W Klein
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA.,Center for Computational Science, Boston University, Boston, Massachusetts 02215, USA
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17
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de Azevedo-Lopes A, de la Rocha AR, de Oliveira PMC, Arenzon JJ. Dynamical cluster size heterogeneity. Phys Rev E 2020; 101:012108. [PMID: 32069589 DOI: 10.1103/physreve.101.012108] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2019] [Indexed: 11/07/2022]
Abstract
Only recently has the essential role of the percolation critical point been considered on the dynamical properties of connected regions of aligned spins (domains) after a sudden temperature quench. In equilibrium, it is possible to resolve the contribution to criticality by the thermal and percolative effects (on finite lattices, while in the thermodynamic limit they merge at a single critical temperature) by studying the cluster size heterogeneity, H_{eq}(T), a measure of how different the domains are in size. We extend this equilibrium measure here and study its temporal evolution, H(t), after driving the system out of equilibrium by a sudden quench in temperature. We show that this single parameter is able to detect and well-separate the different time regimes, related to the two timescales in the problem, namely the short percolative and the long coarsening one.
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Affiliation(s)
- Amanda de Azevedo-Lopes
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil
| | - André R de la Rocha
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil
| | - Paulo Murilo C de Oliveira
- Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-340 Boa Viagem, Niterói, RJ, Brazil.,Instituto Nacional de Ciência e Tecnologia-Sistemas Complexos, 22290-180 Rio de Janeiro RJ, Brazil
| | - Jeferson J Arenzon
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil.,Instituto Nacional de Ciência e Tecnologia-Sistemas Complexos, 22290-180 Rio de Janeiro RJ, Brazil
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18
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Bianco V, Franzese G. Hydrogen bond correlated percolation in a supercooled water monolayer as a hallmark of the critical region. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.04.090] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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19
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Tomita Y. Measurement of entanglement entropy in the two-dimensional Potts model using wavelet analysis. Phys Rev E 2018; 97:052128. [PMID: 29906832 DOI: 10.1103/physreve.97.052128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2017] [Indexed: 11/07/2022]
Abstract
A method is introduced to measure the entanglement entropy using a wavelet analysis. Using this method, the two-dimensional Haar wavelet transform of a configuration of Fortuin-Kasteleyn (FK) clusters is performed. The configuration represents a direct snapshot of spin-spin correlations since spin degrees of freedom are traced out in FK representation. A snapshot of FK clusters loses image information at each coarse-graining process by the wavelet transform. It is shown that the loss of image information measures the entanglement entropy in the Potts model.
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Affiliation(s)
- Yusuke Tomita
- College of Engineering, Shibaura Institute of Technology, Saitama, Saitama 337-8570, Japan
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20
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Kobayashi M, Cugliandolo LF. Quench dynamics of the three-dimensional U(1) complex field theory: Geometric and scaling characterizations of the vortex tangle. Phys Rev E 2017; 94:062146. [PMID: 28085364 DOI: 10.1103/physreve.94.062146] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 11/07/2022]
Abstract
We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II superconductors, magnetic materials, and aspects of cosmology. We characterize the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls off algebraically and we associate it to a geometric percolation transition that we characterize in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermodynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach toward a state that, within numerical accuracy, shares many features with the one at the percolation threshold; a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops; and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.
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Affiliation(s)
- Michikazu Kobayashi
- Department of Physics, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan
| | - Leticia F Cugliandolo
- Sorbonne Universités, Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique et Hautes Energies UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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21
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Binder K, Virnau P. Overview: Understanding nucleation phenomena from simulations of lattice gas models. J Chem Phys 2016; 145:211701. [DOI: 10.1063/1.4959235] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 9, D-55099 Mainz, Germany
| | - Peter Virnau
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 9, D-55099 Mainz, Germany
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22
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Timonin PN, Chitov GY. Exploring percolative landscapes: Infinite cascades of geometric phase transitions. Phys Rev E 2016; 93:012102. [PMID: 26871019 DOI: 10.1103/physreve.93.012102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Indexed: 11/07/2022]
Abstract
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.
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Affiliation(s)
- P N Timonin
- Physics Research Institute, Southern Federal University, 344090, Stachki 194, Rostov-on-Don, Russia
| | - Gennady Y Chitov
- Department of Physics, Laurentian University, Sudbury, Ontario, Canada P3E 2C6
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23
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Sastre F, Benavides AL, Torres-Arenas J, Gil-Villegas A. Microcanonical ensemble simulation method applied to discrete potential fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:033303. [PMID: 26465582 DOI: 10.1103/physreve.92.033303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2015] [Indexed: 06/05/2023]
Abstract
In this work we extend the applicability of the microcanonical ensemble simulation method, originally proposed to study the Ising model [A. Hüller and M. Pleimling, Int. J. Mod. Phys. C 13, 947 (2002)0129-183110.1142/S0129183102003693], to the case of simple fluids. An algorithm is developed by measuring the transition rates probabilities between macroscopic states, that has as advantage with respect to conventional Monte Carlo NVT (MC-NVT) simulations that a continuous range of temperatures are covered in a single run. For a given density, this new algorithm provides the inverse temperature, that can be parametrized as a function of the internal energy, and the isochoric heat capacity is then evaluated through a numerical derivative. As an illustrative example we consider a fluid composed of particles interacting via a square-well (SW) pair potential of variable range. Equilibrium internal energies and isochoric heat capacities are obtained with very high accuracy compared with data obtained from MC-NVT simulations. These results are important in the context of the application of the Hüller-Pleimling method to discrete-potential systems, that are based on a generalization of the SW and square-shoulder fluids properties.
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Affiliation(s)
- Francisco Sastre
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, AP E-143, CP 37150, León, Mexico
| | - Ana Laura Benavides
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, AP E-143, CP 37150, León, Mexico
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040, Madrid, Spain
| | - José Torres-Arenas
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, AP E-143, CP 37150, León, Mexico
| | - Alejandro Gil-Villegas
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León de la Universidad de Guanajuato, AP E-143, CP 37150, León, Mexico
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24
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de la Rocha AR, de Oliveira PMC, Arenzon JJ. Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042113. [PMID: 25974445 DOI: 10.1103/physreve.91.042113] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2015] [Indexed: 06/04/2023]
Abstract
A measure of cluster size heterogeneity (H), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d=2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed.
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Affiliation(s)
- André R de la Rocha
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
| | - Paulo Murilo C de Oliveira
- Instituto Mercosul de Estudos Avançados, Universidade Federal da Integração Latino Americana, Foz do Iguaçu, Paraná, Brazil
- Instituto de Física, Universidade Federal Fluminense, Niterói, Rio de Janiero, Brazil
| | - Jeferson J Arenzon
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
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25
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Oliveira CLN, Araújo NAM, Andrade JS, Herrmann HJ. Explosive electric breakdown due to conducting-particle deposition on an insulating substrate. PHYSICAL REVIEW LETTERS 2014; 113:155701. [PMID: 25375722 DOI: 10.1103/physrevlett.113.155701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Indexed: 06/04/2023]
Abstract
We introduce a theoretical model to investigate the electric breakdown of a substrate on which highly conducting particles are adsorbed and desorbed with a probability that depends on the local electric field. We find that, by tuning the relative strength q of this dependence, the breakdown can change from continuous to explosive. Precisely, in the limit in which the adsorption probability is the same for any finite voltage drop, we can map our model exactly onto the q-state Potts model and thus the transition to a jump occurs at q = 4. In another limit, where the adsorption probability becomes independent of the local field strength, the traditional bond percolation model is recovered. Our model is thus an example of a possible experimental realization exhibiting a truly discontinuous percolation transition.
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Affiliation(s)
- Cláudio L N Oliveira
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
| | - Nuno A M Araújo
- Computational Physics, IfB, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal and Centro de Física Teórica e Computacional, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa, Portugal
| | - José S Andrade
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil and Computational Physics, IfB, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland
| | - Hans J Herrmann
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil and Computational Physics, IfB, ETH Zürich, Hönggerberg, CH-8093 Zürich, Switzerland
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26
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Brown A, Edelman A, Rocks J, Coniglio A, Swendsen RH. Monte Carlo renormalization-group analysis of percolation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:043307. [PMID: 24229304 DOI: 10.1103/physreve.88.043307] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2013] [Indexed: 06/02/2023]
Abstract
We describe a Monte Carlo renormalization group approach to the calculation of critical behavior for percolation models. This approach can be utilized to determine the renormalized bond probabilities and the values of the critical exponents. We illustrate the method for two-dimensional bond percolation, but the method is also applicable to other percolation models and other dimensions.
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Affiliation(s)
- Albert Brown
- Physics Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15217, USA
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27
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Elçi EM, Weigel M. Efficient simulation of the random-cluster model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:033303. [PMID: 24125381 DOI: 10.1103/physreve.88.033303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2013] [Indexed: 06/02/2023]
Abstract
The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.
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Affiliation(s)
- Eren Metin Elçi
- Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, United Kingdom and Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
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28
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Preisler Z, Vissers T, Smallenburg F, Munaò G, Sciortino F. Phase diagram of one-patch colloids forming tubes and lamellae. J Phys Chem B 2013; 117:9540-7. [PMID: 23902159 DOI: 10.1021/jp404053t] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
We numerically calculate the equilibrium phase diagram of one-patch particles with 30% patch coverage. It has been previously shown that in the fluid phase these particles organize into extremely long tubelike aggregates (G. Munaò et al. Soft Matter 2013, 9, 2652). Here, we demonstrate by means of free-energy calculations that such a disordered tube phase, despite forming spontaneously from the fluid phase below a density-dependent temperature, is always metastable against a lamellar crystal. We also show that a crystal of infinitely long packed tubes is thermodynamically stable, but only at high pressure. The full phase diagram of the model, beside the fluid phase, displays four different stable crystals. A gas-liquid critical point, and hence a liquid phase, is not detected.
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Affiliation(s)
- Zdenek Preisler
- Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy
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29
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Schmitz F, Virnau P, Binder K. Monte Carlo tests of nucleation concepts in the lattice gas model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:053302. [PMID: 23767652 DOI: 10.1103/physreve.87.053302] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2013] [Indexed: 06/02/2023]
Abstract
The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasistatic) cluster (droplet) growth over a free energy barrier ΔF(*), constructed in terms of a balance of surface and bulk term of a critical droplet of radius R(*), implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius R=R(*). For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. Using the definition of physical clusters based on the Fortuin-Kasteleyn mapping, the time dependence of the cluster size distribution is studied for quenching experiments in the kinetic Ising model and the cluster size ℓ(*) where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the physical clusters have a volume consistent with the estimates from the lever rule. Geometrical clusters (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60% of the critical temperature, where the cluster shape is nonspherical. We show how the chemical potential can be used to numerically estimate ΔF(*) also for nonspherical cluster shapes.
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Affiliation(s)
- Fabian Schmitz
- Institute of Physics, Johannes Gutenberg Universität Mainz, D-55122 Mainz, Germany
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30
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Posé N, Araújo NAM, Herrmann HJ. Conductivity of Coniglio-Klein clusters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:051140. [PMID: 23214771 DOI: 10.1103/physreve.86.051140] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2012] [Revised: 09/26/2012] [Indexed: 06/01/2023]
Abstract
We performed numerical simulations of the q-state Potts model to compute the reduced conductivity exponent t/ν for the critical Coniglio-Klein clusters in two dimensions, for values of q in the range [1,4]. At criticality, at least for q<4, the conductivity scales as C(L) ~ L(-t/ν), where t and ν are, respectively, the conductivity and correlation length exponents. For q=1, 2, 3, and 4, we followed two independent procedures to estimate t/ν. First, we computed directly the conductivity at criticality and obtained t/ν from the size dependence. Second, using the relation between conductivity and transport properties, we obtained t/ν from the diffusion of a random walk on the backbone of the cluster. From both methods, we estimated t/ν to be 0.986 ± 0.012, 0.877 ± 0.014, 0.785 ± 0.015, and 0.658 ± 0.030, for q=1, 2, 3, and 4, respectively. We also evaluated t/ν for noninteger values of q and propose the conjecture 40 gt/ν = 72 + 20 g - 3g(2) for the dependence of the reduced conductivity exponent on q, in the range 0 ≤ q ≤ 4, where g is the Coulomb gas coupling.
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Affiliation(s)
- Nicolas Posé
- Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, CH-8093 Zurich, Switzerland.
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31
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Lundow PH, Campbell IA. Fortuin-Kasteleyn and damage-spreading transitions in random-bond Ising lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041121. [PMID: 23214543 DOI: 10.1103/physreve.86.041121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2012] [Revised: 07/10/2012] [Indexed: 06/01/2023]
Abstract
The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures T(FK)(p) and T(DS)(p) are studied on random-bond Ising models of dimensions 2-5 and as functions of the ferromagnetic interaction probability p; the conjecture that T(DS)(p)~T(FK)(p) is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn T(FK)(p) transition line and the Nishimori line [p(NL,FK),T(NL,FK)]. There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration [p(NL,FK)], the damage spreading T(DS)(p) is found to be equal to T(FK)(p) to within 0.1%. For the other dimensions, however, T(DS)(p) is observed to be systematically a few percent lower than T(FK)(p).
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Affiliation(s)
- P H Lundow
- Department of Theoretical Physics, Kungliga Tekniska högskolan, SE-106 91 Stockholm, Sweden
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32
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Jo WS, Yi SD, Baek SK, Kim BJ. Cluster-size heterogeneity in the two-dimensional Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:032103. [PMID: 23030964 DOI: 10.1103/physreve.86.032103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2012] [Indexed: 06/01/2023]
Abstract
We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents obtained via the finite-size scaling analysis are shown to be consistent with theoretical values of the fractal dimension d(f) and the Fisher exponent τ for the cluster distribution. We also point out that strong finite-size effects exist due to the geometric nature of the cluster-size heterogeneity.
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Affiliation(s)
- Woo Seong Jo
- BK21 Physics Research Division and Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
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Abstract
Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and systematically preventing the occupation of bridges, namely elements that, if occupied, would provide global connectivity, we disclose that bridges hide a new tricritical point at an occupation fraction p = pc, where pc is the percolation threshold of random percolation. For any value of p in the interval pc < p ≤ 1, our results show that the set of bridges has a fractal dimension dBB ≈ 1.22 in two dimensions. In the limit p → 1, a self-similar fracture is revealed as a singly connected line that divides the system in two domains. We then unveil how several seemingly unrelated physical models tumble into the same universality class and also present results for higher dimensions.
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Chandra AK. Percolation in a kinetic opinion exchange model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021149. [PMID: 22463194 DOI: 10.1103/physreve.85.021149] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2011] [Revised: 01/31/2012] [Indexed: 05/31/2023]
Abstract
We study the percolation transition of the geometrical clusters in the square-lattice LCCC model [a kinetic opinion exchange model introduced by Lallouache, Chakrabarti, Chakraborti, and Chakrabarti, Phys. Rev. E 82, 056112 (2010)] with the change in conviction and influencing parameter. The cluster is comprised of the adjacent sites having an opinion value greater than or equal to a prefixed threshold value of opinion (Ω). The transition point is different from that obtained for the transition of the order parameter (average opinion value) found by Lallouache et al. Although the transition point varies with the change in the threshold value of the opinion, the critical exponents for the percolation transition obtained from the data collapses of the maximum cluster size, the cluster size distribution, and the Binder cumulant remain the same. The exponents are also independent of the values of conviction and influencing parameters, indicating the robustness of this transition. The exponents do not match any other known percolation exponents (e.g., the static Ising, dynamic Ising, and standard percolation). This means that the LCCC model belongs to a separate universality class.
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Affiliation(s)
- Anjan Kumar Chandra
- Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India.
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35
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Oleinikova A, Brovchenko I. Hydrogen-bonded network of hydration water around model solutes. Phys Chem Chem Phys 2012; 14:5686-94. [DOI: 10.1039/c2cp00062h] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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36
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Bianco V, Iskrov S, Franzese G. Understanding the role of hydrogen bonds in water dynamics and protein stability. J Biol Phys 2012; 38:27-48. [PMID: 23277668 PMCID: PMC3285729 DOI: 10.1007/s10867-011-9235-7] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2011] [Accepted: 08/07/2011] [Indexed: 11/30/2022] Open
Abstract
The mechanisms of cold and pressure denaturation of proteins are a matter of debate, but it is commonly accepted that water plays a fundamental role in the process. It has been proposed that the denaturation process is related to an increase of hydrogen bonds among hydration water molecules. Other theories suggest that the causes of denaturation are the density fluctuations of surface water, or the destabilization of hydrophobic contacts as a consequence of water molecule inclusions inside the protein, especially at high pressures. We review some theories that have been proposed to give insight into this problem, and we describe a coarse-grained model of water that compares well with experiments for proteins' hydration water. We introduce its extension for a homopolymer in contact with the water monolayer and study it by Monte Carlo simulations in an attempt to understand how the interplay of water cooperativity and interfacial hydrogen bonds affects protein stability.
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Affiliation(s)
- Valentino Bianco
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
| | - Svilen Iskrov
- École Normale Supérieure de Cachan, 61, avenue du Président Wilson, 94235 Cachan cedex, France
| | - Giancarlo Franzese
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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Weigel M. Connected-component identification and cluster update on graphics processing units. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036709. [PMID: 22060531 DOI: 10.1103/physreve.84.036709] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2011] [Indexed: 05/31/2023]
Abstract
Cluster identification tasks occur in a multitude of contexts in physics and engineering such as, for instance, cluster algorithms for simulating spin models, percolation simulations, segmentation problems in image processing, or network analysis. While it has been shown that graphics processing units (GPUs) can result in speedups of two to three orders of magnitude as compared to serial codes on CPUs for the case of local and thus naturally parallelized problems such as single-spin flip update simulations of spin models, the situation is considerably more complicated for the nonlocal problem of cluster or connected component identification. I discuss the suitability of different approaches of parallelization of cluster labeling and cluster update algorithms for calculations on GPU and compare to the performance of serial implementations.
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Affiliation(s)
- Martin Weigel
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany.
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38
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Biswas S, Kundu A, Chandra AK. Dynamical percolation transition in the Ising model studied using a pulsed magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:021109. [PMID: 21405820 DOI: 10.1103/physreve.83.021109] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2010] [Revised: 11/30/2010] [Indexed: 05/30/2023]
Abstract
We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class.
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Affiliation(s)
- Soumyajyoti Biswas
- Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700064, India.
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39
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Hu H, Deng Y, Blöte HWJ. Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensional XY model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011124. [PMID: 21405678 DOI: 10.1103/physreve.83.011124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2010] [Indexed: 05/30/2023]
Abstract
We study a percolation problem on a substrate formed by two-dimensional XY spin configurations using Monte Carlo methods. For a given spin configuration, we construct percolation clusters by randomly choosing a direction x in the spin vector space, and then placing a percolation bond between nearest-neighbor sites i and j with probability p(ij)=max(0,1-e(-2Ks(i)(x)s(j)(x))), where K>0 governs the percolation process. A line of percolation thresholds K(c)(J) is found in the low-temperature range J≥J(c), where J>0 is the XY coupling strength. Analysis of the correlation function g(p)(r), defined as the probability that two sites separated by a distance r belong to the same percolation cluster, yields algebraic decay for K≥K(c)(J), and the associated critical exponent depends on J and K. Along the threshold line K(c)(J), the scaling dimension for g(p) is, within numerical uncertainties, equal to 1/8. On this basis, we conjecture that the percolation transition along the K(c)(J) line is of the Berezinskii-Kosterlitz-Thouless type.
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Affiliation(s)
- Hao Hu
- Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei, China
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40
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Tavares JM, Teixeira PIC, Telo da Gama MM, Sciortino F. Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions. J Chem Phys 2010; 132:234502. [DOI: 10.1063/1.3435346] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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41
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Tartaglia P, Sciortino F. Association of limited valence patchy particles in two dimensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:104108. [PMID: 21389442 DOI: 10.1088/0953-8984/22/10/104108] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We investigate theoretically the phase behavior of particles with limited valence in two dimensions, by solving the first-order Wertheim theory form. As previously found for three dimensions, in two dimensions also the valence has a strong impact on the phase diagram, controlling the location of the gas-liquid coexistence. On decreasing the valence, the critical density and temperature decrease while the region of gas-liquid instability shrinks and vanishes. At low temperatures, the system reaches its ground state with particles forming a fully bonded network which spans the system.
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Affiliation(s)
- Piero Tartaglia
- Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Rome, Italy
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42
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Sciortino F, Giacometti A, Pastore G. A numerical study of one-patch colloidal particles: from square-well to Janus. Phys Chem Chem Phys 2010; 12:11869-77. [DOI: 10.1039/c0cp00504e] [Citation(s) in RCA: 117] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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43
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Oleinikova A, Brovchenko I. Percolation Threshold of Water in Ideal Binary Mixture. Z PHYS CHEM 2009. [DOI: 10.1524/zpch.2009.6055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Abstract
Percolation transitions of water and solute molecules in an ideal completely miscible aqueous solution are studied by computer simulations. Three concentration ranges with different kinds of water and solute clustering can be distinguished. An infinite water network, present in pure liquid water, breaks at some solute concentration. Accordingly, the infinite network of solute molecules, present in pure liquid solute, breaks upon addition of water. At ambient and high temperatures, there is a concentration range were both components are below their respective percolation thresholds and there are no water or solute infinite networks. The existence of such concentration range is a characteristic of a completely miscible binary mixture. Upon supercooling, the threshold concentrations decrease and simultaneous existence of the infinite networks of water and of solute becomes possible. The presence of two inter-penetrating infinite networks of molecules may be one of the conditions required for the liquid-liquid transition of one-component isotropic fluid.
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Russo J, Tartaglia P, Sciortino F. Reversible gels of patchy particles: role of the valence. J Chem Phys 2009; 131:014504. [PMID: 19586107 DOI: 10.1063/1.3153843] [Citation(s) in RCA: 111] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We simulate a binary mixture of colloidal patchy particles with two and three patches, respectively, for several relative concentrations and hence relative average valences. For these limited-valence systems, it is possible to reach low temperatures, where the lifetime of the patch-patch interactions becomes longer than the observation time without encountering phase separation in a colloid-poor (gas) and a colloid rich (liquid) phase. The resulting arrested state is a fully connected long-lived network where particles with three patches provide the branching points connecting chains of two-patch particles. We investigate the effect of the valence on the structural and dynamic properties of the resulting gel and attempt to provide a theoretical description of the formation and of the resulting gel structure based on a combination of the Wertheim theory for associated liquids and the Flory-Stockmayer approach for modeling chemical gelation.
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Affiliation(s)
- John Russo
- Dipartimento di Fisica and INFM-CNR-SOFT, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy.
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45
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Manor A, Shnerb NM. Multiplicative noise and second order phase transitions. PHYSICAL REVIEW LETTERS 2009; 103:030601. [PMID: 19659259 DOI: 10.1103/physrevlett.103.030601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2009] [Revised: 05/26/2009] [Indexed: 05/28/2023]
Abstract
The scale-free distribution of cluster sizes in continuous phase transitions is linked to the law of proportional effect. A numerical study of a two-dimensional Ising model suggests that a cluster size undergoes a multiplicative birth-death process. At the transition the ratio between birth and death rates approaches unity for large clusters, and the resulting steady state shows a power-law behavior. The percolation dynamic, on the other hand, yields a geometric phase transition without ergodicity breaking, where large-scale merging and splitting of clusters dominate the distribution. Instead of short-range birth-death jumps, the percolation transition is characterized by Lévi flights along the cluster-size axis.
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Affiliation(s)
- Alon Manor
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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46
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Ding C, Deng Y, Guo W, Blöte HWJ. Percolation and critical O(n) loop configurations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:061118. [PMID: 19658484 DOI: 10.1103/physreve.79.061118] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2009] [Indexed: 05/28/2023]
Abstract
We study a percolation problem based on critical loop configurations of the O(n) loop model on the honeycomb lattice. We define dual clusters as groups of sites on the dual triangular lattice that are not separated by a loop, and investigate the bond-percolation properties of these dual clusters. The universal properties at the percolation threshold are argued to match those of Kasteleyn-Fortuin random clusters in the critical Potts model. This relation is checked numerically by means of cluster simulations of several O(n) models in the range 1<or=n<or=2. The simulation results include the percolation threshold for several values of n, as well as the universal exponents associated with bond dilution and the size distribution of the diluted clusters at the percolation threshold. Our numerical results for the exponents are in agreement with existing Coulomb-gas results for the random-cluster model, which confirms the relation between both models. We discuss the renormalization flow of the bond-dilution parameter p as a function of n, and provide an expression that accurately describes a line of unstable fixed points as a function of n, corresponding with the percolation threshold. Furthermore, the renormalization scenario indicates the existence, in a p versus n diagram, of another line of fixed points at p=1, which is stable with respect to p.
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Affiliation(s)
- Chengxiang Ding
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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47
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Kami N, Ikeda H. Topological transition in dynamic complex networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:056112. [PMID: 19518526 DOI: 10.1103/physreve.79.056112] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2008] [Revised: 03/06/2009] [Indexed: 05/27/2023]
Abstract
Using a network model involving statistical mechanics we study the topological transition of complex networks with evolving wiring structure. The evolution rule of our network model contains both a structuring effect originated in a wiring decision metric (local clustering coefficient) and a randomizing effect due to thermal fluctuation. Monte Carlo simulation results show a dramatic topological transition between nonclustered networks and clustered networks in response to changes in the degree of randomness.
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Affiliation(s)
- Nobuharu Kami
- Department of Electrical Engineering, Stanford University, Stanford, California 94305-9510, USA.
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49
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Brovchenko I, Burri RR, Krukau A, Oleinikova A, Winter R. Intrinsic thermal expansivity and hydrational properties of amyloid peptide Aβ42 in liquid water. J Chem Phys 2008; 129:195101. [DOI: 10.1063/1.3012562] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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50
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Bianchi E, Tartaglia P, Zaccarelli E, Sciortino F. Theoretical and numerical study of the phase diagram of patchy colloids: ordered and disordered patch arrangements. J Chem Phys 2008; 128:144504. [PMID: 18412456 DOI: 10.1063/1.2888997] [Citation(s) in RCA: 116] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.
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Affiliation(s)
- Emanuela Bianchi
- Dipartimento di Fisica and INFM-CRS-SMC, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy
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