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

Dynamical critical exponent of a nonequilibrium Ising model

B. C. S. Grandi, W. Figueiredo

Published Nov 1, 1996• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.54.4722

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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.
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.
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.
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.
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.
This paper studies, by means of Monte Carlo simulations, an open ferromagnetic spin-3/2 Ashkin-Teller model defined on a square lattice. This model can be viewed as the superposition of two Ising models which are coupled by a four-spin interaction strength K4while in each Ising model, the nearest-neighbor interaction constant is K2. The model is here submitted to two stochastic dynamics that consist of two processes; the first one is the Glauber dynamics which simulates the contact of the system with a heat bath at temperature T and the second one is the Kawasaki dynamics which simulates the continuous energy flux into the system from an external source. The Glauber single-spin flip process happens with the probability p while the Kawasaki spin-exchange process between neighboring sites occurs with the probability q = 1− p. The temperature-dependence of the system magnetizations for fixed coupling constants and lattice anisotropy has been thoroughly investigated. Several thermodynamic phases and phase transitions have been obtained as well as multicritical points. When the Kawasaki dynamics becomes dominant, self-organized antiferromagnetic phases are generated. Several phase diagrams have been devised to illustrate model thermodynamic properties.