Two-temperature nonequilibrium Ising models: Critical behavior and universality

We study a class of two-dimensional (2D) nonequilibrium Ising models based on competing dynamics induced by contact with heat baths at two different temperatures. We make a comparative study of the nonequilibrium versions of Metropolis, heat bath--Glauber, and Swendsen-Wang dynamics, and focus on their critical behavior in order to understand their universality classes. We present 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. We show that the bond version of the Swendsen-Wang update algorithm can be mapped into an equilibrium model at an effective temperature.