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Jami P, Chaudhuri P, Dasgupta C, Ghosal A. Effect of disorder on phases across two-dimensional thermal melting. Phys Rev E 2024; 109:L062101. [PMID: 39021015 DOI: 10.1103/physreve.109.l062101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Accepted: 04/11/2024] [Indexed: 07/20/2024]
Abstract
We study melting in a two-dimensional system of classical particles with Gaussian-core interactions in disordered environments. The pure system validates the conventional two-step melting with a hexatic phase intervening between the solid and the liquid. This picture is modified in the presence of pinning impurities. A random distribution of pinning centers forces a hexaticlike low-temperature phase that transits into a liquid at a single melting temperature T_{m}^{RP}. In contrast, pinning centers located at randomly chosen sites of a perfect crystal anchor a solid at low temperatures which undergoes a direct transition to the liquid at T_{m}^{CP}. Thus, the two-step melting is lost in either case of disorder. We discuss the characteristics of melting depending on the nature of the impurities.
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2
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Tsiok EN, Fomin YD, Gaiduk EA, Ryzhov VN. Structural transition in two-dimensional Hertzian spheres in the presence of random pinning. Phys Rev E 2021; 103:062612. [PMID: 34271643 DOI: 10.1103/physreve.103.062612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 06/03/2021] [Indexed: 11/07/2022]
Abstract
Using molecular dynamics simulation we have investigated the influence of random pinning on the phase diagram and melting scenarios of a two-dimensional system with the Hertz potential for α=5/2. It has been shown that random pinning can cardinally change the mechanism of first-order transition between the different crystalline phases (triangular and square) by virtue of generating hexatic and tetratic phases: a triangular crystal to hexatic transition is of the continuous Berezinskii-Kosterlitz-Thouless (BKT) type, a hexatic to tetratic transition is of first order, and finally, there is a continuous BKT-type transition from tetratic to the square crystal.
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Affiliation(s)
- E N Tsiok
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - Yu D Fomin
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - E A Gaiduk
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - V N Ryzhov
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
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3
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H A, Chaudhuri P. Dense hard disk ordering: influence of bidispersity and quenched disorder. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:414001. [PMID: 32521523 DOI: 10.1088/1361-648x/ab9b52] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 06/10/2020] [Indexed: 06/11/2023]
Abstract
Using Monte Carlo simulations, the impact on structural ordering in two-dimensional systems via the interplay of size bidispersity and quenched disorder in the form of an externally applied spatially random potential, is studied for a system of hard disks. By scanning across a wide range of dense packing fractions, size ratios and roughness of the applied potential, the phase diagram is constructed, which demonstrates that both quenched and size disorders shift the onset of translational order to higher packings, while maintaining the presence of the intermediate hexatic phase. At larger disorder strengths, the signatures of structural order are absent within the range of investigated packing fractions. Further, the dynamics with increasing potential strength is analysed for the mono-component system to obtain a spatio-temporal description of the melting process. Finally, the influence of the externally rough field on the Mermin-Wagner fluctuations, characteristic to two-dimensional systems, is investigated.
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Affiliation(s)
- Arjun H
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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4
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Gámez F, Rodríguez-Almeida LF, Trejos VM. Thermodynamics of two-dimensional molecular fluids: Discrete perturbation theory and Monte Carlo simulations. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2019.112293] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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5
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Gaiduk EA, Fomin Y, Tsiok EN, Ryzhov VN. The influence of random pinning on the melting scenario of two-dimensional soft-disk systems. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1607917] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- E. A. Gaiduk
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
| | - Yu.D. Fomin
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
| | - E. N. Tsiok
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
| | - V. N. Ryzhov
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, Russia
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6
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Roy I, Dutta S, Roy Choudhury AN, Basistha S, Maccari I, Mandal S, Jesudasan J, Bagwe V, Castellani C, Benfatto L, Raychaudhuri P. Melting of the Vortex Lattice through Intermediate Hexatic Fluid in an a-MoGe Thin Film. PHYSICAL REVIEW LETTERS 2019; 122:047001. [PMID: 30768342 DOI: 10.1103/physrevlett.122.047001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2018] [Revised: 08/03/2018] [Indexed: 06/09/2023]
Abstract
The hexatic fluid refers to a phase in between a solid and a liquid that has short-range positional order but quasi-long-range orientational order. In the celebrated theory of Berezinskii, Kosterlitz, and Thouless and subsequently refined by Halperin, Nelson, and Young, it was predicted that a two-dimensional hexagonal solid can melt in two steps: first, through a transformation from a solid to a hexatic fluid, which retains quasi-long-range orientational order; and then from a hexatic fluid to an isotropic liquid. In this Letter, using a combination of real space imaging and transport measurements, we show that the two-dimensional vortex lattice in an a-MoGe thin film follows this sequence of melting as the magnetic field is increased. Identifying the signatures of various transitions on the bulk transport properties of the superconductor, we construct a vortex phase diagram for a two-dimensional superconductor.
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Affiliation(s)
- Indranil Roy
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Surajit Dutta
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | | | - Somak Basistha
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Ilaria Maccari
- ISC-CNR and Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro, 5, 00185 Rome, Italy
| | - Soumyajit Mandal
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - John Jesudasan
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Vivas Bagwe
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Claudio Castellani
- ISC-CNR and Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro, 5, 00185 Rome, Italy
| | - Lara Benfatto
- ISC-CNR and Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro, 5, 00185 Rome, Italy
| | - Pratap Raychaudhuri
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
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7
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Liu C, Gao W, Yang B, Zhang S. Disorder-Induced Topological State Transition in Photonic Metamaterials. PHYSICAL REVIEW LETTERS 2017; 119:183901. [PMID: 29219571 DOI: 10.1103/physrevlett.119.183901] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2017] [Indexed: 06/07/2023]
Abstract
The topological state transition has been widely studied based on the quantized topological band invariant such as the Chern number for the system without intense randomness that may break the band structures. We numerically demonstrate the disorder-induced state transition in the photonic topological systems for the first time. Instead of applying the ill-defined topological band invariant in a disordered system, we utilize an empirical parameter to unambiguously illustrate the state transition of the topological metamaterials. Before the state transition, we observe a robust surface state with well-confined electromagnetic waves propagating unidirectionally, immune to the disorder from permittivity fluctuation up to 60% of the original value. During the transition, a hybrid state composed of a quasiunidirectional surface mode and intensively localized hot spots is established, a result of the competition between the topological protection and Anderson localization.
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Affiliation(s)
- Changxu Liu
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Wenlong Gao
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Biao Yang
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Shuang Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
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8
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Sándor C, Libál A, Reichhardt C, Olson Reichhardt CJ. Dewetting and spreading transitions for active matter on random pinning substrates. J Chem Phys 2017; 146:204903. [PMID: 28571342 DOI: 10.1063/1.4983344] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that sterically interacting self-propelled disks in the presence of random pinning substrates exhibit transitions among a variety of different states. In particular, from a phase separated cluster state, the disks can spread out and homogeneously cover the substrate in what can be viewed as an example of an active matter wetting transition. We map the location of this transition as a function of activity, disk density, and substrate strength, and we also identify other phases including a cluster state, coexistence between a cluster and a labyrinth wetted phase, and a pinned liquid. Convenient measures of these phases include the cluster size, which dips at the wetting-dewetting transition, and the fraction of sixfold coordinated particles, which drops when dewetting occurs.
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Affiliation(s)
- Cs Sándor
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - A Libál
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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9
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Mehboudi M, Dorio AM, Zhu W, van der Zande A, Churchill HOH, Pacheco-Sanjuan AA, Harriss EO, Kumar P, Barraza-Lopez S. Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers. NANO LETTERS 2016; 16:1704-12. [PMID: 26866878 DOI: 10.1021/acs.nanolett.5b04613] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.
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Affiliation(s)
- Mehrshad Mehboudi
- Department of Physics, University of Arkansas , Fayetteville, Arkansas 72701, United States
| | - Alex M Dorio
- Department of Physics, University of Arkansas , Fayetteville, Arkansas 72701, United States
| | - Wenjuan Zhu
- Department of Electrical and Computer Engineering, University of Illinois , Urbana, Illinois 61820, United States
| | - Arend van der Zande
- Department of Mechanical Science and Engineering, University of Illinois , Urbana, Illinois 61820, United States
| | - Hugh O H Churchill
- Department of Physics, University of Arkansas , Fayetteville, Arkansas 72701, United States
| | | | - Edmund O Harriss
- Department of Mathematical Sciences, University of Arkansas , Fayetteville, Arkansas 72701, United States
| | - Pradeep Kumar
- Department of Physics, University of Arkansas , Fayetteville, Arkansas 72701, United States
| | - Salvador Barraza-Lopez
- Department of Physics, University of Arkansas , Fayetteville, Arkansas 72701, United States
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10
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Tsiok EN, Dudalov DE, Fomin YD, Ryzhov VN. Random pinning changes the melting scenario of a two-dimensional core-softened potential system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032110. [PMID: 26465429 DOI: 10.1103/physreve.92.032110] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Indexed: 06/05/2023]
Abstract
In experiments two-dimensional systems are realized mainly on solid substrates, which introduce quenched disorder due to some inherent defects. The defects of substrates influence the melting scenario of the systems and have to be taken into account in the interpretation of experimental results. We present the results of molecular dynamics simulations of a two-dimensional system with a core-softened potential in which a small fraction of the particles is pinned, inducing quenched disorder. Ppotentials of this type are widely used for the qualitative description of systems with waterlike anomalies. In our previous publications it was shown that the system demonstrates an anomalous melting scenario: at low densities the system melts through two continuous transitions in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory with an intermediate hexatic phase, while at high densities the conventional first-order melting transition takes place. We find that the well-known disorder-induced widening of the hexatic phase occurs at low densities, while in the high-density part of the phase diagram random pinning transforms the first-order melting into two transitions: a continuous KTHNY-like solid-hexatic transition and a first-order hexatic-isotropic liquid transition.
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Affiliation(s)
- E N Tsiok
- Institute for High Pressure Physics RAS, Kaluzhskoe shosse 14, 142190 Troitsk, Moscow, Russia
| | - D E Dudalov
- Institute for High Pressure Physics RAS, Kaluzhskoe shosse 14, 142190 Troitsk, Moscow, Russia
| | - Yu D Fomin
- Institute for High Pressure Physics RAS, Kaluzhskoe shosse 14, 142190 Troitsk, Moscow, Russia
- Moscow Institute of Physics and Technology, 141700 Moscow, Russia
| | - V N Ryzhov
- Institute for High Pressure Physics RAS, Kaluzhskoe shosse 14, 142190 Troitsk, Moscow, Russia
- Moscow Institute of Physics and Technology, 141700 Moscow, Russia
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11
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Reichhardt C, Ray D, Reichhardt CJO. Collective transport properties of driven Skyrmions with random disorder. PHYSICAL REVIEW LETTERS 2015; 114:217202. [PMID: 26066455 DOI: 10.1103/physrevlett.114.217202] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2014] [Indexed: 06/04/2023]
Abstract
We use particle-based simulations to examine the static and driven collective phases of Skyrmions interacting with random quenched disorder. We show that nondissipative effects due to the Magnus term reduce the depinning threshold and strongly affect the Skyrmion motion and the nature of the dynamic phases. The quenched disorder causes the Hall angle to become drive dependent in the moving Skyrmion phase, while different flow regimes produce distinct signatures in the transport curves. For weak disorder, the Skyrmions form a pinned crystal and depin elastically, while for strong disorder the system forms a pinned amorphous state that depins plastically. At high drives the Skyrmions can dynamically reorder into a moving crystal, with the onset of reordering determined by the strength of the Magnus term.
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Affiliation(s)
- C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - D Ray
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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12
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Ozeki Y, Yotsuyanagi S, Sakai T, Echinaka Y. Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022122. [PMID: 25353437 DOI: 10.1103/physreve.89.022122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2013] [Indexed: 06/04/2023]
Abstract
The critical exponents are estimated for the gauge glass model in two dimensions, in which only the Kosterlitz-Thouless (KT) phase appears in the low-temperature regime. The nonequilibrium relaxation method is applied to estimate the transition temperature and critical exponents: the static exponent η and the dynamical exponent z. Since the system exhibits criticality in the whole KT phase, we estimate the exponents on the boundary as well as inside the KT phase. The static exponent η depends on both the temperature and the strength of randomness, while the dynamical one z is almost constant throughout the KT phase, including the boundary.
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Affiliation(s)
- Yukiyasu Ozeki
- Department of Engineering Science, Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
| | - Satoshi Yotsuyanagi
- Department of Applied Physics and Chemistry, Graduate School of Electro-Communications, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
| | - Takuya Sakai
- Department of Applied Physics and Chemistry, Graduate School of Electro-Communications, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
| | - Yuki Echinaka
- Department of Engineering Science, Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
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13
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Horn T, Deutschländer S, Löwen H, Maret G, Keim P. Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062305. [PMID: 24483442 DOI: 10.1103/physreve.88.062305] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2013] [Indexed: 06/03/2023]
Abstract
Using both video microscopy of superparamagnetic colloidal particles confined in two dimensions and corresponding computer simulations of repulsive parallel dipoles, we study the formation of fluctuating orientational clusters and topological defects in the context of the KTHNY-like melting scenario under quenched disorder. We analyze cluster densities, average cluster sizes, and the population of noncluster particles, as well as the development of defects, as a function of the system temperature and disorder strength. In addition, the probability distribution of clustering and orientational order is presented. We find that the well-known disorder-induced widening of the hexatic phase can be traced back to the distinct development characteristics of clusters and defects along the melting transitions from the solid phase to the hexatic phase to the isotropic fluid.
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Affiliation(s)
- Tobias Horn
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | | | - Hartmut Löwen
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Georg Maret
- Fachbereich für Physik, Universität Konstanz, D-78464 Konstanz, Germany
| | - Peter Keim
- Fachbereich für Physik, Universität Konstanz, D-78464 Konstanz, Germany
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14
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Deutschländer S, Horn T, Löwen H, Maret G, Keim P. Two-dimensional melting under quenched disorder. PHYSICAL REVIEW LETTERS 2013; 111:098301. [PMID: 24033073 DOI: 10.1103/physrevlett.111.098301] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2013] [Indexed: 06/02/2023]
Abstract
We study the influence of quenched disorder on the two-dimensional melting behavior of superparamagnetic colloidal particles, using both video microscopy and computer simulations of repulsive parallel dipoles. Quenched disorder is introduced by pinning a fraction of the particles to an underlying substrate. We confirm the occurrence of the Kosterlitz-Thouless-Halperin-Nelson-Young scenario and observe an intermediate hexatic phase. While the fluid-hexatic transition remains largely unaffected by disorder, the hexatic-solid transition shifts to lower temperatures with increasing disorder. This results in a significantly broadened stability range of the hexatic phase. In addition, we observe spatiotemporal critical(like) fluctuations, which are consistent with the continuous character of the phase transitions. Characteristics of first-order transitions are not observed.
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15
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Wilms D, Deutschländer S, Siems U, Franzrahe K, Henseler P, Keim P, Schwierz N, Virnau P, Binder K, Maret G, Nielaba P. Effects of confinement and external fields on structure and transport in colloidal dispersions in reduced dimensionality. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:464119. [PMID: 23114365 DOI: 10.1088/0953-8984/24/46/464119] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
In this work, we focus on low-dimensional colloidal model systems, via simulation studies and also some complementary experiments, in order to elucidate the interplay between phase behavior, geometric structures and transport properties. In particular, we try to investigate the (nonlinear!) response of these very soft colloidal systems to various perturbations: uniform and uniaxial pressure, laser fields, shear due to moving boundaries and randomly quenched disorder. We study ordering phenomena on surfaces or in monolayers by Monte Carlo computer simulations of binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. Weak external fields allow a controlled tuning of the miscibility of the mixture. We discuss the laser induced de-mixing for the three different possible couplings to the external potential. The structural behavior of hard spheres interacting with repulsive screened Coulomb or dipolar interaction in 2D and 3D narrow constrictions is investigated using Brownian dynamics simulations. Due to misfits between multiples of the lattice parameter and the channel widths, a variety of ordered and disordered lattice structures have been observed. The resulting local lattice structures and defect probabilities are studied for various cross sections. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior. Additionally, in an experimental system of dipolar colloidal particles confined by gravity on a solid substrate we investigate the effect of pinning on the dynamics of a two-dimensional colloidal liquid. This work contains sections reviewing previous work by the authors as well as new, unpublished results. Among the latter are detailed studies of the phase boundaries of the de-mixing regime in binary systems in external light fields, configurations for shear induced effects at structured walls, studies on the effect of confinement on the structures and defect densities in three-dimensional systems, the effect of confinement and barriers on two-dimensional flow and diffusion, and the effect of pinning sites on the diffusion.
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Affiliation(s)
- D Wilms
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany.
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16
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Granato E, Ramos JAP, Achim CV, Lehikoinen J, Ying SC, Ala-Nissila T, Elder KR. Glassy phases and driven response of the phase-field-crystal model with random pinning. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:031102. [PMID: 22060323 DOI: 10.1103/physreve.84.031102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2011] [Revised: 07/10/2011] [Indexed: 05/31/2023]
Abstract
We study the structural correlations and the nonlinear response to a driving force of a two-dimensional phase-field-crystal model with random pinning. The model provides an effective continuous description of lattice systems in the presence of disordered external pinning centers, allowing for both elastic and plastic deformations. We find that the phase-field crystal with disorder assumes an amorphous glassy ground state, with only short-ranged positional and orientational correlations, even in the limit of weak disorder. Under increasing driving force, the pinned amorphous-glass phase evolves into a moving plastic-flow phase and then, finally, a moving smectic phase. The transverse response of the moving smectic phase shows a vanishing transverse critical force for increasing system sizes.
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Affiliation(s)
- E Granato
- Laboratório Associado de Sensores e Materiais, Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, SP, Brazil
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17
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Yotsuyanagi S, Suemitsu Y, Ozeki Y. Effects of discreteness on gauge glass models in two and three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:041138. [PMID: 19518204 DOI: 10.1103/physreve.79.041138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2008] [Indexed: 05/27/2023]
Abstract
The q-state clock gauge glass model is studied to see the effect of discreteness on the Kosterlitz-Thouless (KT) transition and the ferromagnetic (FM) critical phenomenon in random systems. The nonequilibrium relaxation analysis is applied. In two dimensions, the successive transitions of paramagnetic (PM), KT, and FM phases are investigated along the Nishimori line for q=6, 8, 10, 12, 14, 16, and 1024 (recognized as infinity) cases. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all q values. The lower transition temperature is found to be proportional to 1/q2. In three dimensions, the critical behavior of the PM-FM transition is studied along the Nishimori line for q=6, 8, 16, and 1024 cases. It is found that the spin discreteness is irrelevant, and the transition belongs to the same universality class as in the (continuous) XY case.
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Affiliation(s)
- Satoshi Yotsuyanagi
- Department of Physics and Chemistry, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
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Reichhardt C, Reichhardt CJO. Disordering transitions and peak effect in polydisperse particle systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:041401. [PMID: 18517611 DOI: 10.1103/physreve.77.041401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2007] [Revised: 11/20/2007] [Indexed: 05/26/2023]
Abstract
We show numerically that in a binary system of Yukawa particles, a dispersity-driven disordering transition occurs. In the presence of quenched disorder this disordering transition coincides with a marked increase in the depinning threshold, known as a peak effect. We find that the addition of poorly pinned particles can increase the overall pinning in the sample by increasing the amount of topological disorder present. If the quenched disorder is strong enough to create a significant amount of topological disorder in the monodisperse system, addition of a poorly pinned species generates further disorder but does not produce a peak in the depinning force. Our results indicate that for binary mixtures, optimal pinning occurs for topological defect fraction densities from 0.2 to 0.25. For defect densities below this range, the system retains orientational order. We determine the effect of the pinning density, strength, and radius on the depinning peak and find that the peak effect is more pronounced in weakly pinning systems.
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Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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19
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Yun YJ, Baek IC, Choi MY. Phase transition and critical dynamics in site-diluted Josephson-junction arrays. PHYSICAL REVIEW LETTERS 2006; 97:215701. [PMID: 17155750 DOI: 10.1103/physrevlett.97.215701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2006] [Indexed: 05/12/2023]
Abstract
Measurements of the IV characteristics of site-diluted Josephson-junction arrays have revealed intriguing effects of percolative disorder on the phase transition and the vortex dynamics in a two-dimensional XY system. Different from other types of phase transitions, the Kosterlitz-Thouless transition was eliminated with the introduction of percolative disorder far below the percolation threshold. Even after the Kosterlitz-Thouless order had been removed, the system remained superconducting at low temperatures by establishing a different type of order. Near the percolation threshold, evidence was found that, as a consequence of the underlying fractal structure, the critical dynamics of the phase degrees of freedom persisted down to zero temperature.
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Affiliation(s)
- Young-Je Yun
- Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746, Korea
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20
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Chen L, Deem MW. Two-dimensional diffusion in the presence of topological disorder. ACTA ACUST UNITED AC 2003; 68:021107. [PMID: 14524953 DOI: 10.1103/physreve.68.021107] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2002] [Revised: 06/05/2003] [Indexed: 11/07/2022]
Abstract
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder leads to a finite reduction of the diffusion coefficient. Renormalization group theory and numerical simulations suggest that longer-ranged disorder, such as that from randomly placed dislocations or random disclinations with no net disclinicity, leads to subdiffusion at long times.
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Affiliation(s)
- Ligang Chen
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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21
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Nazarenko VG, Nych AB, Lev BI. Crystal structure in nematic emulsion. PHYSICAL REVIEW LETTERS 2001; 87:075504. [PMID: 11497900 DOI: 10.1103/physrevlett.87.075504] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2001] [Indexed: 05/23/2023]
Abstract
We describe the experimental observation of a crystal structure formed by glycerol droplets suspended in a nematic liquid crystal. The structure exhibits a high density hexagonal ordering. We have experimentally observed a noticeable interaction between droplets with tangential boundary conditions. Within the scope of known models we discuss the nature of appropriate mechanisms of the interaction.
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Affiliation(s)
- V G Nazarenko
- Institute of Physics, National Academy of Science of Ukraine, 46 Prospekt Nauky, 03039, Kyiv, Ukraine.
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22
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Castillo HE, Le Doussal P. Freezing of dynamical exponents in low dimensional random media. PHYSICAL REVIEW LETTERS 2001; 86:4859-4862. [PMID: 11384366 DOI: 10.1103/physrevlett.86.4859] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2000] [Indexed: 05/23/2023]
Abstract
A particle in a random potential with logarithmic correlations in dimensions d = 1,2 is shown to undergo a dynamical transition at T(dyn)>0. In d = 1 exact results show T(dyn) = T(c), the static glass transition temperature, and that the dynamical exponent changes from z(T) = 2+2(T(c)/T)(2) at high T to z(T) = 4T(c)/T in the glass phase. The same formulas are argued to hold in d = 2. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In d = 1 a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics, relevant to dislocation motion experiments.
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Affiliation(s)
- H E Castillo
- CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Cedex 05, Paris, France
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23
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Carpentier D, Le Doussal P. Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:026110. [PMID: 11308545 DOI: 10.1103/physreve.63.026110] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2000] [Indexed: 05/23/2023]
Abstract
We study via renormalization group (RG), numerics, exact bounds, and qualitative arguments the equilibrium Gibbs measure of a particle in a d-dimensional Gaussian random potential with translationally invariant logarithmic spatial correlations. We show that for any d>/=1 it exhibits a transition at T=T(c)>0. The low-temperature glass phase has a nontrivial structure, being dominated by a few distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists only in this "marginal glass" case (energy fluctuation exponent straight theta=0) and disappears if correlations grow faster (single ground-state dominance straight theta>0) or slower (high-temperature phase). The associated extremal statistics problem for correlated energy landscapes exhibits universal features which we describe using a nonlinear Kolmogorov (KPP) RG equation. These include the tails of the distribution of the minimal energy (or free energy) and the finite-size corrections, which are universal. The glass transition is closely related to Derrida's random energy models. In d=2, the connection between this problem and Liouville and sinh-Gordon models is discussed. The glass transition of the particle exhibits interesting similarities with the weak- to strong-coupling transition in Liouville (c=1 barrier) and with a transition that we conjecture for the sinh-Gordon model, with correspondence in some exact results and RG analysis. Glassy freezing of the particle is associated with the generation under RG of new local operators and of nonsmooth configurations in Liouville. Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar "quasilocalized" regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.
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Affiliation(s)
- D Carpentier
- Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
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Li M, Johnson WL, Goddard WA. Evidence of hexatic phase formation in two-dimensional Lennard-Jones binary arrays. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:12067-12072. [PMID: 9985063 DOI: 10.1103/physrevb.54.12067] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Tang LH. Vortex statistics in a disordered two-dimensional XY model. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:3350-3366. [PMID: 9986235 DOI: 10.1103/physrevb.54.3350] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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26
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Korshunov SE, Nattermann T. Absence of reentrance in superconducting arrays with positional disorder. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:2746-2755. [PMID: 9983785 DOI: 10.1103/physrevb.53.2746] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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