Non-equilibrium phase transitions in the two-temperature Ising model with Kawasaki dynamics

Abstract

Phase transitions of the two-finite temperature Ising model on a square lattice are investigated by using a position space renormalization group (PSRG) transformation. Different finite temperatures, Tx and Ty, and also different timescale constants, αx and αy for spin exchanges in the x and y directions define the dynamics of the non-equilibrium system. The critical surface of the system is determined by RG flows as a function of these exchange parameters. The Onsager critical point (when the two temperatures are equal) and the critical temperature for the limit when the other temperature is infinite, previously studied by the Monte Carlo method, are obtained. In addition, two steady-state fixed points which correspond to the non-equilibrium phase transition are presented. These fixed points yield the different universality class properties of the non-equilibrium phase transitions.

Nonequilibrium statistical mechanics of a two-temperature Ising ring with conserved dynamics

“…Nearly all studies involve dynamics which are (essentially) translationally invariant, while many involve anisotropy. There are a number of examples of work being done on systems coupling the two baths to every spin or every other spin (for Glauber dynamics in d ≥ 1) [28][29][30][31][32][33][34][35][36]. In the case of the alternating coupling, the two dimensional model was found to exhibit an order-disorder phase transition that belonged to the Ising universality class.…”