Non-equilibrium steady state phase transitions of various statistical models

Abstract

Non-equilibrium phase transitions of a number of systems are investigated by several methods. These systems are in contact with thermal baths with different temperatures and taken to be driven to the non-equilibrium limits by spin exchange (Kawasaki) dynamics. First of all, the criticality of the two-finite temperature spin-1/2 Ising model with a conserved order parameter on a square lattice is studied through a real space renormalization group transformation. The dynamics of the nonequilibrium system are characterized by means of different temperatures (Tx and Ty), and also different time-scale constants, (αx and αy) for spin exchanges in the x and y directions. Based on the RG flows, the critical surface of the system is obtained as a function of these exchange parameters. This is the first study in which the full critical surface displaying various universality classes of this system is reported. Secondly, steady state phase transitions of the eight-vertex model, formulated by two interlaced two-dimensional Ising models on square lattices, are studied through four independent Monte Carlo simulations, each with 60 × 106 Monte Carlo steps on N × N lattices with N = 32, 40, 80, 100. To obtain an isotropic system, the spin exchanges are considered to occur within the sublattices. We observe non-universal behavior for non-equilibrium transitions around the equilibrium transitions, and Ising like behavior when one of the bath temperature becomes very large.