Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Critical exponents of the Ising model with competing Glauber and Kawasaki dynamics

B. C. S. Grandi, W. Figueiredo

Published May 1, 1996• 28 citations
Publisher

Abstract

The two-dimensional Ising model with competing Glauber and Kawasaki dynamics is studied by Monte Carlo simulations. We show that the model exhibits the phenomenon of self-organization when the Kawasaki dynamics is the dominant one. For this model we show that the values of the critical exponents calculated at the stationary states are in accordance with the exact ones known for the equilibrium Ising model. These results give support to the idea that the equilibrium and nonequilibrium Ising models, which exhibit up-down symmetry, belong to the same universality class. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.53.5484

Related papers

Dynamical critical exponent of a nonequilibrium Ising model

B. C. S. Grandi, W. Figueiredo

The dynamical critical exponent z of the two-dimensional Ising model with competing Glauber and Kawasaki processes is evaluated by Monte Carlo simulations. This model exhibits the phenomenon of self-organization when the Kawasaki dynamics is the dominant one. We have calculated the exponent z as a function of the parameter that controls the competition between the two processes. Our calculations are performed at the phase boundary that separates the nonequilibrium ordered and disordered phases. The values of z we obtain are around z=2 for all values of the competing parameter. When the Glauber dynamics is the only one present the value of z is in agreement with most recent calculations. \textcopyright{} 1996 The American Physical Society.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 1996•10 citations

Phase transitions in the kinetic Ising model with competing dynamics

Attila Szolnoki

We study the nonequilibrium phase diagram and critical properties of a two-dimensional kinetic Ising model with competing Glauber and Kawasaki dynamics suggested by Tome and de Oliveira [Phys. Rev. A 40, 6643 (1989)]. The role of the Kawasaki dynamics, chosen with probability 1-p, is to simulate a permanent energy flux into the system. The theoretical prediction for the phase diagram is improved significantly by using four- and six-point dynamical mean-field approximations. Monte Carlo simulations support that the ferromagnetic-paramagnetic phase transition changes from second to first order for sufficiently small p. The antiferromagnetic phase is found to be stable for a nonzero value of p even at T=0.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 2000•27 citations

Monte Carlo simulation of an antiferromagnetic Ising model at two competing temperatures

B. C. S. Grandi, W. Figueiredo

We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•May 1, 1999•1 citation

Monte Carlo renormalization-group studies of kinetic Ising models

M. Cemal Yalabık, J. D. Gunton

The dynamic Monte Carlo renormalization group is applied to the two-dimensional Kawasaki and three-dimensional Glauber models. Our best "matching" results for the Kawasaki model yield a value of $z=3.80$ for the dynamical exponent, as compared with the exact value $z=3.75$. This provides strong confirmation for the validity of this method. The results for the Glauber model are less accurate, but our estimate of $z\ensuremath{\simeq}2.08$ is in reasonable agreement with the $\ensuremath{\epsilon}$ expansion.

Physical review. B, Condensed matter•Jan 1, 1982•48 citations

Critical dynamics for one-dimensional models

F. Leyvraz, Naeem Jan

A plausible argument using the concepts of dynamic renormalisation group is used to derive the dynamical exponent z of the one-dimensional q=2, 3 and 4 Potts and four-state clock models. The exact result (z=2) for the Ising model with Glauber dynamics is recovered and in addition the authors find that the q=3, 4 Potts and four-state clock models belong to the same universality class. Moreover they find that z=3.05+or-0.1 for the (q=2) Potts model with Kawasaki dynamics in agreement with the z=4- eta prediction of Halperin, Hohenberg and Ma (1974). A simple qualitative derivation is also given.

Journal of Physics A Mathematical and General•Mar 11, 1986•10 citations

TWO-TEMPERATURE NON-EQUILIBRIUM ISING MODELS

Pablo Tamayo, Rajan Gupta, Francis J. Alexander

We present results from a computational study of a class of 2D two-temperature non-equilibrium Ising models. In these systems the dynamics is a local competition of two equilibrium dynamics at different temperatures. We analyzed non-equilibrium versions of Metropolis, heat bath/Glauber and Swendsen-Wang dynamics and found strong evidence that some of these dynamics have the same critical exponents and belong to the same universality class as the equilibrium 2D Ising model.

International Journal of Modern Physics C•Jun 1, 1996•2 citations
The two-dimensional Ising model with competing Glauber and Kawasaki dynamics is studied by Monte Carlo simulations. We show that the model exhibits the phenomenon of self-organization when the Kawasaki dynamics is the dominant one. For this model we show that the values of the critical exponents calculated at the stationary states are in accordance with the exact ones known for the equilibrium Ising model. These results give support to the idea that the equilibrium and nonequilibrium Ising models, which exhibit up-down symmetry, belong to the same universality class. \textcopyright{} 1996 The American Physical Society.
The dynamical critical exponent z of the two-dimensional Ising model with competing Glauber and Kawasaki processes is evaluated by Monte Carlo simulations. This model exhibits the phenomenon of self-organization when the Kawasaki dynamics is the dominant one. We have calculated the exponent z as a function of the parameter that controls the competition between the two processes. Our calculations are performed at the phase boundary that separates the nonequilibrium ordered and disordered phases. The values of z we obtain are around z=2 for all values of the competing parameter. When the Glauber dynamics is the only one present the value of z is in agreement with most recent calculations. \textcopyright{} 1996 The American Physical Society.
We study the nonequilibrium phase diagram and critical properties of a two-dimensional kinetic Ising model with competing Glauber and Kawasaki dynamics suggested by Tome and de Oliveira [Phys. Rev. A 40, 6643 (1989)]. The role of the Kawasaki dynamics, chosen with probability 1-p, is to simulate a permanent energy flux into the system. The theoretical prediction for the phase diagram is improved significantly by using four- and six-point dynamical mean-field approximations. Monte Carlo simulations support that the ferromagnetic-paramagnetic phase transition changes from second to first order for sufficiently small p. The antiferromagnetic phase is found to be stable for a nonzero value of p even at T=0.
We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.
The dynamic Monte Carlo renormalization group is applied to the two-dimensional Kawasaki and three-dimensional Glauber models. Our best "matching" results for the Kawasaki model yield a value of z=3.80z=3.80z=3.80 for the dynamical exponent, as compared with the exact value z=3.75z=3.75z=3.75. This provides strong confirmation for the validity of this method. The results for the Glauber model are less accurate, but our estimate of $z\ensuremath{\simeq}2.08$ is in reasonable agreement with the $\ensuremath{\epsilon}$ expansion.
A plausible argument using the concepts of dynamic renormalisation group is used to derive the dynamical exponent z of the one-dimensional q=2, 3 and 4 Potts and four-state clock models. The exact result (z=2) for the Ising model with Glauber dynamics is recovered and in addition the authors find that the q=3, 4 Potts and four-state clock models belong to the same universality class. Moreover they find that z=3.05+or-0.1 for the (q=2) Potts model with Kawasaki dynamics in agreement with the z=4- eta prediction of Halperin, Hohenberg and Ma (1974). A simple qualitative derivation is also given.