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Bhattacharyya R, Sen Gupta B. Kinetics of phase separation and aging dynamics of segregating fluid mixtures in the presence of quenched disorder. SOFT MATTER 2024; 20:2969-2977. [PMID: 38470361 DOI: 10.1039/d4sm00204k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
Quenched or frozen-in structural disorder is ubiquitous in real experimental systems. Much of the progress is achieved in understanding the phase separation of such systems using the diffusion-driven coarsening in an Ising model with quenched disorder. But there is a paucity of research on the phase-separation kinetics in fluids with quenched disorder. In this paper, we present results from a detailed molecular dynamics simulation, showing the effects of randomly placed localized impurities on the phase separation kinetics of binary fluid mixtures. Two different models are offered for representing the impurities. We observe a dramatic slowing down in the pattern formation with increasing impurity concentration. This sluggish domain growth kinetics follows a power-law with a disorder-dependent exponent. The correlation function and structure factor show a non-Porod behavior, indicating the roughening of the domain interfaces. We have also studied the effect of quenched disorder on the aging dynamics by calculating the two-time order parameter auto correlation function and find that the Fisher and Huse scaling law holds good in the presence of quenched disorder.
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Affiliation(s)
- Rounak Bhattacharyya
- Institute for Theoretical Physics and BioQuant, Heidelberg University, Heidelberg 69120, Germany
| | - Bhaskar Sen Gupta
- Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India.
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Bhattacharyya R, Gupta BS. Effect of annealed disorder on phase separation kinetics and aging phenomena in fluid mixtures. Phys Rev E 2021; 104:054612. [PMID: 34942791 DOI: 10.1103/physreve.104.054612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2021] [Accepted: 11/03/2021] [Indexed: 11/07/2022]
Abstract
We use state-of-the-art molecular dynamics simulations to study the effects of annealed disorder on the phase-separating kinetics and aging phenomena of a segregating binary fluid mixture. In the presence of disorder, we observe a dramatic slowing down in the phase separation dynamics. The domain growth follows the power law with a disorder-dependent exponent. Due to the energetically favorable positions, the domain boundary roughens, which modifies the correlation function and structure factor to a non-Porod behavior. The correlation function and structure factor provide clear evidence that superuniversality does not hold in our system. The role of annealed disorder on the nonequilibrium aging dynamics is studied qualitatively by computing the two-time order-parameter autocorrelation function. The decay of the correlation function slows down significantly with the disorder. This quantity exhibits scaling laws with respect to the ratio of the domain length at the observation time and the age of the system. We find the scaling laws hold good for the disordered system and are therefore robust and generic to such segregating fluid mixtures.
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Affiliation(s)
- Rounak Bhattacharyya
- Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
| | - Bhaskar Sen Gupta
- Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
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Chatterjee S, Sutradhar S, Puri S, Paul R. Ordering kinetics in a q-state random-bond clock model: Role of vortices and interfaces. Phys Rev E 2020; 101:032128. [PMID: 32290025 DOI: 10.1103/physreve.101.032128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 03/02/2020] [Indexed: 11/07/2022]
Abstract
In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the nonconserved two-dimensional random-bond q-state clock model (RBCM) deriving from a pure clock model [Chatterjee et al., Phys. Rev. E 98, 032109 (2018)10.1103/PhysRevE.98.032109]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper (T_{c}^{1}) and lower (T_{c}^{2}) phase transition temperatures decrease with bond randomness strength ε. Effect of ε on the nonequilibrium coarsening dynamics is investigated following independent rapid quenches in the quasi-long-range ordered (QLRO, T_{c}^{2}<T<T_{c}^{1}) regime and long-range ordered (LRO, T<T_{c}^{2}) regime at temperature T. We report that the dynamical scaling of the correlation function and structure factor is independent of ε and the presence of quenched disorder slows down domain coarsening. Coarsening dynamics in both LRO and QLRO regimes are further characterized by power-law growth with disorder-dependent exponents within our simulation timescales. The growth exponents in the LRO regime decrease from 0.5 in the pure case to 0.22 in the maximum disordered case, whereas the corresponding change in the QLRO regime happens from 0.45 to 0.38. We further explored the coarsening dynamics in the bond-diluted clock model and, in both the models, the effect of the disorder is more significant for the quench in the LRO regime compared to the QLRO regime.
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Affiliation(s)
- Swarnajit Chatterjee
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | | | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Raja Paul
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India
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Singh A, Singh A, Chakraborti A. Effect of bond-disorder on the phase-separation kinetics of binary mixtures: A Monte Carlo simulation study. J Chem Phys 2017; 147:124902. [PMID: 28964037 DOI: 10.1063/1.5004563] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For a higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov power-law growth in all the cases.
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Affiliation(s)
- Awaneesh Singh
- Department of Physics, Institute of Chemical Technology, Mumbai 400019, India
| | - Amrita Singh
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Anirban Chakraborti
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Corberi F, Kumar M, Puri S, Lippiello E. Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration. Phys Rev E 2017; 95:062136. [PMID: 28709286 DOI: 10.1103/physreve.95.062136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2017] [Indexed: 06/07/2023]
Abstract
We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction a of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of a, a<a_{f}. In an intermediate range, a_{f}<a<a_{a}, the system is paramagnetic, with spin-glass order expected right at zero temperature. For even larger values, a>a_{a}, an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of a. We show that different amounts of frustration, tuned by a, affect the dynamical properties in a highly nontrivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e., algebraic, when spin-glass order is prevailing. An interpretation is given in terms of the different nature of phase space.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E.R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Manoj Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Eugenio Lippiello
- Dipartimento di Matematica e Fisica, University of Campania "L. Vanvitelli", viale Lincoln, 5 81100 Caserta, Italy
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Corberi F, Cugliandolo LF, Insalata F, Picco M. Coarsening and percolation in a disordered ferromagnet. Phys Rev E 2017; 95:022101. [PMID: 28297910 DOI: 10.1103/physreve.95.022101] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2016] [Indexed: 06/06/2023]
Abstract
By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder (either random bonds or random fields) we show that a critical percolation structure forms at an early stage. This structure is then rendered more and more compact by the ensuing coarsening process. Our results are compared to the nondisordered case, where a similar phenomenon is observed, and they are interpreted within a dynamical scaling framework.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
- INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
| | - Leticia F Cugliandolo
- Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Ferdinando Insalata
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
- Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Marco Picco
- Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Ahmad S, Puri S, Das SK. Phase separation of fluids in porous media: a molecular dynamics study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:040302. [PMID: 25375423 DOI: 10.1103/physreve.90.040302] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2014] [Indexed: 06/04/2023]
Abstract
We present comprehensive molecular dynamics results for phase-separation kinetics of fluids in a porous medium. This system is modeled by a symmetric Lennard-Jones fluid mixture with a quenched random field. The presence of disorder slows down domain growth from power-law to a logarithmic form. It also modifies the correlation functions and structure factors which characterize the morphology. In particular, the structure-factor tail shows a non-Porod behavior, which is the consequence of scattering from rough interfaces.
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Affiliation(s)
- Shaista Ahmad
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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Corberi F, Lippiello E, Mukherjee A, Puri S, Zannetti M. Scaling in the aging dynamics of the site-diluted Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042129. [PMID: 24229138 DOI: 10.1103/physreve.88.042129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2013] [Indexed: 06/02/2023]
Abstract
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the nondiluted system, there exist two disorder fixed points, characterized by logarithmic and power-law growth of the ordered domains. This structure gives rise to a rich scaling behavior, with an interesting crossover due to the competition between fixed points, and violation of superuniversality.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy
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Corberi F, Lippiello E, Mukherjee A, Puri S, Zannetti M. Crossover in growth law and violation of superuniversality in the random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021141. [PMID: 22463186 DOI: 10.1103/physreve.85.021141] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2011] [Indexed: 05/31/2023]
Abstract
We study the nonconserved phase-ordering dynamics of the d=2,3 random-field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three dimensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, we find the exponent in the preasymptotic power law to be disorder dependent, rather than being that of the pure system. Furthermore, we find that the autocorrelation function does not display superuniversal behavior. This restores consistency with previous results for the d=1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random-bond Ising model.
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Affiliation(s)
- F Corberi
- Dipartimento di Fisica E. Caianiello and CNISM, Unità di Salerno, Università di Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy
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Paul R, Puri S, Rieger H. Domain growth in Ising systems with quenched disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:061109. [PMID: 16089724 DOI: 10.1103/physreve.71.061109] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2005] [Indexed: 05/03/2023]
Abstract
We present results from extensive Monte Carlo (MC) simulations of domain growth in ferromagnets and binary mixtures with quenched disorder. These are modeled by the random-bond Ising model and the dilute Ising model with either nonconserved (Glauber) spin-flip kinetics or conserved (Kawasaki) spin-exchange kinetics. In all cases, our MC results are consistent with power-law growth with an exponent theta(T, epsilon) which depends on the quench temperature T and the disorder amplitude epsilon. Such exponents arise naturally when the coarsening domains are trapped by energy barriers that grow logarithmically with the domain size. Our MC results show excellent agreement with the predicted dependence of theta(T, epsilon).
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Affiliation(s)
- Raja Paul
- Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
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Tafa K, Puri S, Kumar D. Kinetics of domain growth in systems with local barriers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:046115. [PMID: 11308920 DOI: 10.1103/physreve.63.046115] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2000] [Indexed: 05/23/2023]
Abstract
We study domain growth in spin-1 lattice models having nonconserved spin-flip kinetics with local barriers. Our primary motivation is to model the relaxational behavior of physical systems in which molecular motion is impeded by local kinetic barriers. The kinetic constraint is such that a spin from an up (down) state can flip to a down (up) state only via the zero state, which has a higher energy. We examine how the usual curvature-driven domain growth is affected by these local barriers, and whether the single-spin barriers have a collective effect. This paper presents comprehensive numerical results for phase ordering dynamics in this model using Monte Carlo simulations. We demonstrate dynamical scaling for domain-size distribution functions and spatial correlation functions. We also present results for the time dependence of characteristic length scales and autocorrelation functions. The length-scale behavior is interpreted in terms of the random walk of steps on domain boundaries. Furthermore, we present a simple stochastic model to derive an analytic expression for the autocorrelation function, which exhibits a stretched-exponential behavior over an extended regime-in agreement with our numerical simulations.
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Affiliation(s)
- K Tafa
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Puri S, Parekh N. Non-algebraic domain growth in binary alloys with quenched disorder. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/25/15/020] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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13
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Puri S, Frisch HL. Segregation dynamics of binary mixtures with simple chemical reactions. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/27/18/013] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Puri S, Parekh N. Non-algebraic domain growth for phase ordering dynamics in a random field. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/26/12/018] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Rutenberg AD. Stress-free spatial anisotropy in phase ordering. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:R2181-R2184. [PMID: 9965436 DOI: 10.1103/physreve.54.r2181] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Gyure MF, Harrington ST, Strilka R, Stanley HE. Scaling in late stage spinodal decomposition with quenched disorder. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:4632-4639. [PMID: 9963955 DOI: 10.1103/physreve.52.4632] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Rao M, Chakrabarti A. Kinetics of domain growth in a random-field model in three dimensions. PHYSICAL REVIEW LETTERS 1993; 71:3501-3504. [PMID: 10054993 DOI: 10.1103/physrevlett.71.3501] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Blundell RE, Bray AJ, Sattler S. Absolute test for theories of phase-ordering dynamics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:2476-2480. [PMID: 9960880 DOI: 10.1103/physreve.48.2476] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Takano H, Miyashita S. Ordering process in the kinetic Ising model on the honeycomb lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:7221-7226. [PMID: 10006891 DOI: 10.1103/physrevb.48.7221] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hayakawa H. Phase ordering in random media. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:11696-11702. [PMID: 10005336 DOI: 10.1103/physrevb.47.11696] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Mason N, Pargellis AN, Yurke B. Scaling behavior of two-time correlations in a twisted nematic liquid crystal. PHYSICAL REVIEW LETTERS 1993; 70:190-193. [PMID: 10053725 DOI: 10.1103/physrevlett.70.190] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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