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International Journal of Modern Physics C

TWO-TEMPERATURE NON-EQUILIBRIUM ISING MODELS

Pablo Tamayo, Rajan Gupta, Francis J. Alexander

Published Jun 1, 1996• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0129183196000338

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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.
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.
Abstract. We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath method and with the global Swendsen-Wang algorithm. In both cases, we find qualitatively different dynamic behaviors for the magnetization and Ω, the order parameter of the percolation transition. This may have implications for the recent attempts to describe the dynamics of the QCD phase transition using cluster observables.
We investigate two-dimensional Ising models with a non-Hamiltonian Glauber dynamics. The transition probabilities are expressed in terms of Boltzmann factors depending only on the nearest neighbour spins and the associated bond strengths. However, the bond strength on each lattice edge is two-valued; it assumes different values with respect to the spins at either of its ends. In one of the two models, the bond strength pattern is consistent with the four-fold rotational symmetry of the square lattice. In contrast, a preferred direction is present in the second model. This model can be interpreted in terms of inhomogeneous interactions and temperature such that their ratios, i. e. the couplings, are uniform. Monte Carlo simulations of these models show that the phase transition persists when these two types of non-Hamiltonian dynamics are introduced. Furthermore, our results indicate that both models belong to the Ising universality class.