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Frielinghaus H, Dubey PS, Saha D, Shin E, Holderer O, Sengers JV, Förster S. Random Field Ising Model Criticality in a Complex Binary Liquid System. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:1125. [PMID: 38998729 PMCID: PMC11243101 DOI: 10.3390/nano14131125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2024] [Accepted: 06/28/2024] [Indexed: 07/14/2024]
Abstract
While Ising criticality in classical liquids has been firmly established both theoretically and experimentally, much less is known about criticality in liquids in which the growth of the correlation length is frustrated by finite-size effects. A theoretical approach for dealing with this issue is the random-field Ising model (RFIM). While experimental critical-exponent values have been reported for magnetic samples (here, we consider γ, ν and η), little experimental information is available for critical fluctuations in corresponding liquid systems. In this paper, we present a study on a binary liquid consisting of 3-methyl pyridine and heavy water in a very light-weight porous gel. We find that the experimental results are in agreement with the theoretical predictions from the RFIM.
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Affiliation(s)
- Henrich Frielinghaus
- Forschungszentrum Jülich GmbH, Jülich Center for Neutron Scattering JCNS-4 at MLZ, Lichtenbergstrasse 1, 85747 Garching, Germany
| | - Purushottam S. Dubey
- Forschungszentrum Jülich GmbH, Jülich Center for Neutron Scattering JCNS-4 at MLZ, Lichtenbergstrasse 1, 85747 Garching, Germany
| | - Debasish Saha
- Forschungszentrum Jülich GmbH, Jülich Center for Neutron Scattering JCNS-4 at MLZ, Lichtenbergstrasse 1, 85747 Garching, Germany
| | - Eunjoo Shin
- Korea Atomic Energy Research Institute, 111, Daedeok-daero 989beon-gil, Yuseong-gu, Daejeon 34057, Republic of Korea
| | - Olaf Holderer
- Forschungszentrum Jülich GmbH, Jülich Center for Neutron Scattering JCNS-4 at MLZ, Lichtenbergstrasse 1, 85747 Garching, Germany
| | - Jan V. Sengers
- Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
| | - Stephan Förster
- Forschungszentrum Jülich GmbH, Jülich Center for Neutron Scattering JCNS-1, Leo-Brandt Str., 52425 Jülich, Germany
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2
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Duan Y, Mahault B, Ma YQ, Shi XQ, Chaté H. Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder. PHYSICAL REVIEW LETTERS 2021; 126:178001. [PMID: 33988412 DOI: 10.1103/physrevlett.126.178001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Revised: 01/10/2021] [Accepted: 02/26/2021] [Indexed: 06/12/2023]
Abstract
We show that spatial quenched disorder affects polar active matter in ways more complex and far reaching than heretofore believed. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order.
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Affiliation(s)
- Yu Duan
- National Laboratory of Solid State Microstructures and Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Benoît Mahault
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Yu-Qiang Ma
- National Laboratory of Solid State Microstructures and Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Xia-Qing Shi
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100193, China
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3
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Guiselin B, Berthier L, Tarjus G. Random-field Ising model criticality in a glass-forming liquid. Phys Rev E 2020; 102:042129. [PMID: 33212666 DOI: 10.1103/physreve.102.042129] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 10/07/2020] [Indexed: 11/07/2022]
Abstract
We use computer simulations to investigate the extended phase diagram of a supercooled liquid linearly coupled to a quenched reference configuration. An extensive finite-size scaling analysis demonstrates the existence of a random-field Ising model (RFIM) critical point and of a first-order transition line, in agreement with recent field-theoretical approaches. The dynamics in the vicinity of this critical point resembles the peculiar activated scaling of RFIM-like systems, and the overlap autocorrelation displays a logarithmic stretching. Our study demonstrates RFIM criticality in the thermodynamic limit for a three-dimensional supercooled liquid at equilibrium.
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Affiliation(s)
- Benjamin Guiselin
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France.,Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Gilles Tarjus
- LPTMC, CNRS-UMR 7600, Sorbonne Université, F-75005 Paris, France
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Sampaio Filho CIN, Andrade JS, Herrmann HJ, Moreira AA. Elastic Backbone Defines a New Transition in the Percolation Model. PHYSICAL REVIEW LETTERS 2018; 120:175701. [PMID: 29756808 DOI: 10.1103/physrevlett.120.175701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2018] [Indexed: 06/08/2023]
Abstract
The elastic backbone is the set of all shortest paths. We found a new phase transition at p_{eb} above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in 2D, its fractal dimension is 1.750±0.003, and one obtains a novel set of critical exponents β_{eb}=0.50±0.02, γ_{eb}=1.97±0.05, and ν_{eb}=2.00±0.02, fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. Using Binder's cumulant, we determine, with high precision, the critical probabilities p_{eb} for the triangular and tilted square lattice for site and bond percolation. This transition describes a sudden rigidification as a function of density when stretching a damaged tissue.
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Affiliation(s)
| | - José S Andrade
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
- Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, 8093 Zurich, Switzerland
| | - Hans J Herrmann
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
- Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, 8093 Zurich, Switzerland
| | - André A Moreira
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
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Belov PA, Nazarov AA, Sorokin AO. Determination of the conformal-field-theory central charge by the Wang-Landau algorithm. Phys Rev E 2017; 95:063308. [PMID: 28709307 DOI: 10.1103/physreve.95.063308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2017] [Indexed: 06/07/2023]
Abstract
We present a simple method to estimate the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice model from Monte Carlo simulations. The main idea is to use the Wang-Landau flat-histogram algorithm, which allows us to obtain the free energy of a lattice model on a torus as a function of torus radii. The central charge is calculated with good precision from a free-energy scaling at the critical point. We apply the method to the Ising, tricritical Ising (Blume-Capel), Potts, and site-diluted Ising models, and we also discuss an estimation of the conformal weights.
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Affiliation(s)
- P A Belov
- Department of Physics, St. Petersburg State University, Ulyanovskaya 1, 198504 St. Petersburg, Russia
| | - A A Nazarov
- Department of Physics, St. Petersburg State University, Ulyanovskaya 1, 198504 St. Petersburg, Russia
| | - A O Sorokin
- Petersburg Nuclear Physics Institute NRC Kurchatov Institute, Orlova roscha 1, 188300 Gatchina, Russia
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Albano EV, Luque L, Trobo ML, Binder K. Numerical evidence of hyperscaling violation in wetting transitions of the random-bond Ising model in d=2 dimensions. Phys Rev E 2017; 95:022801. [PMID: 28297842 DOI: 10.1103/physreve.95.022801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Indexed: 06/06/2023]
Abstract
We performed extensive simulations of the random-bond Ising model confined between walls where competitive surface fields act. By properly taking the thermodynamic limit we unambiguously determined wetting transition points of the system, as extrapolation of localization-delocalization transitions of the interface between domains of different orientation driven by the respective fields. The finite-size scaling theory for wetting with short-range fields [E. V. Albano and K. Binder, Phys. Rev. Lett. 109, 036101 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.036101] establishes that the average magnetization of the sample, with critical exponent β, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by γ+2β=ν_{∥}+ν_{⊥} requires β=1/2 (γ=4, ν_{∥}=3, and ν_{⊥}=2), the thermodynamic scaling establishes that Δ_{s}=γ+β, which in contrast requires β=0 (Δ_{s}=4), where γ, ν_{∥}, ν_{⊥}, and Δ_{s} are the critical exponents of the susceptibility, the correlation lengths parallel and perpendicular to the interface, and the gap exponent, respectively. So, we formulate a finite-size scaling theory for wetting without hyperscaling and perform numerical simulations that provide strong evidence of hyperscaling violation (i.e., β=0) and a direct measurement of the susceptibility critical exponent γ/ν_{⊥}=2.0±0.2, in agreement with theoretical results for the strong fluctuation regime of wetting transitions with quenched noise.
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Affiliation(s)
- Ezequiel V Albano
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CCT-CONICET La Plata, UNLP, Calle 59 Nro. 789, (1900) La Plata, Argentina and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina
| | - Luciana Luque
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CCT-CONICET La Plata, UNLP, Calle 59 Nro. 789, (1900) La Plata, Argentina and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina
| | - Marta L Trobo
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CCT-CONICET La Plata, UNLP, Calle 59 Nro. 789, (1900) La Plata, Argentina and Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata, Argentina
| | - Kurt Binder
- Institute für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
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Fytas NG, Martín-Mayor V. Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions. Phys Rev E 2016; 93:063308. [PMID: 27415388 DOI: 10.1103/physreve.93.063308] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Indexed: 06/06/2023]
Abstract
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
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Affiliation(s)
- Nikolaos G Fytas
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Teórica I, Universidad Complutense, E-28040 Madrid, Spain and Instituto de Biocomputación and Física de Sistemas Complejos (BIFI), E-50009 Zaragoza, Spain
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8
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Jack RL, Garrahan JP. Phase Transition for Quenched Coupled Replicas in a Plaquette Spin Model of Glasses. PHYSICAL REVIEW LETTERS 2016; 116:055702. [PMID: 26894718 DOI: 10.1103/physrevlett.116.055702] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2015] [Indexed: 06/05/2023]
Abstract
We study a three-dimensional plaquette spin model whose low temperature dynamics is glassy, due to localized defects and effective kinetic constraints. The thermodynamics of this system is smooth at all temperatures. We show that coupling it to a second system with a fixed (quenched) configuration leads to a phase transition, at finite coupling. The order parameter is the overlap between the copies, and the transition is between phases of low and high overlap. We find critical points whose properties are consistent with random-field Ising universality. We analyze the interfacial free energy cost between the high- and low-overlap states that coexist at (and below) the critical point, and we use this cost as the basis for a finite-size scaling analysis. We discuss these results in the context of mean-field and dynamical facilitation theories of the glass transition.
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Affiliation(s)
- Robert L Jack
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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9
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Kwak W, Jeong J, Lee J, Kim DH. First-order phase transition and tricritical scaling behavior of the Blume-Capel model: A Wang-Landau sampling approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022134. [PMID: 26382370 DOI: 10.1103/physreve.92.022134] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2015] [Indexed: 06/05/2023]
Abstract
We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, yt=1.804(5), yg=0.80(1), and yh=1.925(3), provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.
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Affiliation(s)
- Wooseop Kwak
- Department of Physics, Chosun University, Gwangju 61452, Korea
| | - Joohyeok Jeong
- Department of Physics and Photon Science, School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju 61005, Korea
| | - Juhee Lee
- Department of Physics and Photon Science, School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju 61005, Korea
| | - Dong-Hee Kim
- Department of Physics and Photon Science, School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju 61005, Korea
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10
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Hong H, Chaté H, Tang LH, Park H. Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022122. [PMID: 26382359 DOI: 10.1103/physreve.92.022122] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2015] [Indexed: 06/05/2023]
Abstract
We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of the intrinsic frequencies of oscillators. For a population of size N, we study two ways of sampling the intrinsic frequencies according to the same given unimodal distribution g(ω). In the "random" case, frequencies are generated independently in accordance with g(ω), which gives rise to oscillator number fluctuation within any given frequency interval. In the "regular" case, the N frequencies are generated in a deterministic manner that minimizes the oscillator number fluctuations, leading to quasiuniformly spaced frequencies in the population. We find that the two samplings yield substantially different finite-size properties with clearly distinct scaling exponents. Moreover, the hyperscaling relation between the order parameter and its fluctuations is valid in the regular case, but it is violated in the random case. In this last case, a self-consistent mean-field theory that completely ignores dynamic fluctuations correctly predicts the FSS exponent of the order parameter but not its critical amplitude.
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Affiliation(s)
- Hyunsuk Hong
- Department of Physics and Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 561-756, Korea
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA-Saclay, CNRS UMR 3680, 91191 Gif-sur-Yvette, France
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Lei-Han Tang
- Beijing Computational Science Research Center, Beijing 100084, China
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China
| | - Hyunggyu Park
- School of Physics and QUC, Korea Institute for Advanced Study, Seoul 130-722, Korea
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Binder K, Virnau P, Statt A. Perspective: The Asakura Oosawa model: A colloid prototype for bulk and interfacial phase behavior. J Chem Phys 2014; 141:140901. [DOI: 10.1063/1.4896943] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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12
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Pellicane G, Vink RLC, Russo B, Giaquinta PV. Fluids in porous media: the case of neutral walls. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042131. [PMID: 24229139 DOI: 10.1103/physreve.88.042131] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Indexed: 06/02/2023]
Abstract
The bulk phase behavior of a fluid is typically altered when the fluid is brought into confinement by the walls of a random porous medium. Inside the porous medium, phase-transition points are shifted, or may disappear altogether. A crucial determinant is how the walls interact with the fluid particles. In this work, we consider the situation whereby the walls are neutral with respect to the liquid and vapor phases. In order to realize the condition of strict neutrality, we use a symmetric binary mixture inside a porous medium that interacts identically with mixture species. Monte Carlo simulations are then used to obtain the phase behavior. Our main finding is that, in the presence of the porous medium, a liquid-vapor critical point still exists. At the critical point, the distribution of the order parameter remains scale invariant, but self-averaging is violated. These findings provide further evidence that random confinement by neutral walls induces critical behavior of the random Ising model (i.e., Ising models with dilution type disorder, where the disorder couples to the energy).
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Affiliation(s)
- Giuseppe Pellicane
- School of Chemistry and Physics, University of Kwazulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa and National Institute for Theoretical Physics (NITheP), KZN node, Pietermaritzburg, South Africa
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Sinha S, Mandal PK. Dynamical properties of random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022121. [PMID: 23496474 DOI: 10.1103/physreve.87.022121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2012] [Indexed: 06/01/2023]
Abstract
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.
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Affiliation(s)
- Suman Sinha
- Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.
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Speck T, Vink RLC. Random pinning limits the size of membrane adhesion domains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031923. [PMID: 23030960 DOI: 10.1103/physreve.86.031923] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2012] [Revised: 08/24/2012] [Indexed: 06/01/2023]
Abstract
Theoretical models describing specific adhesion of membranes predict (for certain parameters) a macroscopic phase separation of bonds into adhesion domains. We show that this behavior is fundamentally altered if the membrane is pinned randomly due to, e.g., proteins that anchor the membrane to the cytoskeleton. Perturbations which locally restrict membrane height fluctuations induce quenched disorder of the random-field type. This rigorously prevents the formation of macroscopic adhesion domains following the Imry-Ma argument [Imry and Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction of random-field disorder follows from analytical calculations and is strikingly confirmed in large-scale Monte Carlo simulations. These simulations are based on an efficient composite Monte Carlo move, whereby membrane height and bond degrees of freedom are updated simultaneously in a single move. The application of this move should prove rewarding for other systems also.
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Affiliation(s)
- Thomas Speck
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
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Fischer T, Risselada HJ, Vink RLC. Membrane lateral structure: the influence of immobilized particles on domain size. Phys Chem Chem Phys 2012; 14:14500-8. [PMID: 22782576 DOI: 10.1039/c2cp41417a] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
In experiments on model membranes, formation of large domains of different lipid composition is readily observed. However, no such phase separation is observed in the membranes of intact cells. Instead, small transient inhomogeneities called lipid rafts are expected in these systems. One of the numerous attempts to explain small domains refers to the coupling of the membrane to its surroundings, which leads to the immobilization of some of the membrane molecules. These immobilized molecules then act as static obstacles for the remaining mobile ones. We present detailed Molecular Dynamics simulations demonstrating that this can indeed account for small domains. This confirms previous Monte Carlo studies based on simplified models. Furthermore, by directly comparing domain structures obtained using Molecular Dynamics to Monte Carlo simulations of the Ising model, we demonstrate that domain formation in the presence of obstacles is remarkably insensitive to the details of the molecular interactions.
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Affiliation(s)
- Timo Fischer
- Institute of Theoretical Physics, Georg-August-Universität Göttingen, Göttingen, Germany
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Annunziata MA, Pelissetto A. Fluid–fluid demixing curves for colloid–polymer mixtures in a random colloidal matrix. Mol Phys 2011. [DOI: 10.1080/00268976.2011.622724] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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17
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Tarjus G, Rosinberg ML, Kierlik E, Tissier M. Hierarchical reference theory of critical fluids in disordered porous media. Mol Phys 2011. [DOI: 10.1080/00268976.2011.620024] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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18
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Fischer T, Vink RLC. Fluids with quenched disorder: scaling of the free energy barrier near critical points. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:234117. [PMID: 21613708 DOI: 10.1088/0953-8984/23/23/234117] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In the context of Monte Carlo simulations, the analysis of the probability distribution P(L)(m) of the order parameter m, as obtained in simulation boxes of finite linear extension L, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, P(L)(m) becomes scale-invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of P(L)(m) at the peaks (P(L, max)) and the value at the minimum in between (P(L, min)) becomes L-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead ΔF(L) := ln(P(L, max)/P(L, min)) proportional to L(θ) should be observed, where θ > 0 is the 'violation of hyperscaling' exponent. Since θ is substantially non-zero, the scaling of ΔF(L) with system size should be easily detectable in simulations. For two fluid models with quenched disorder, ΔF(L) versus L was measured and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random field Ising model.
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Affiliation(s)
- T Fischer
- Institute of Theoretical Physics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
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Fischer T, Vink RLC. Domain formation in membranes with quenched protein obstacles: Lateral heterogeneity and the connection to universality classes. J Chem Phys 2011; 134:055106. [DOI: 10.1063/1.3530587] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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Fytas NG, Theodorakis PE. Universality in disordered systems: the case of the three-dimensional random-bond Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:062101. [PMID: 21230691 DOI: 10.1103/physreve.82.062101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2010] [Indexed: 05/30/2023]
Abstract
We study the critical behavior of the d=3 Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed by the same universality class as the site- and bond-diluted models, clearly distinct from that of the pure model, thus providing a complete set of universality in disordered systems.
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Affiliation(s)
- Nikolaos G Fytas
- Department of Materials Science, University of Patras, Patras 26504, Greece.
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