Eur. Phys. J. B (2012) 85: 398
https://doi.org/10.1140/epjb/e2012-30726-5

Regular Article

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

Phase diagram from position space renormalization group transformation

Department of Physics, Bilkent University, Bilkent, 06800 Ankara, Turkey

^a e-mail: yalabik@fen.bilkent.edu.tr

Received: 6 August 2012
Received in final form: 4 October 2012
Published online: 3 December 2012

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, T_x and T_y, and also different time-scale constants, α_x and α_y 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.