Non-equilibrium phase transition in a two-temperature lattice gas

A two-temperature lattice gas model with repulsive nearest-neighbour interactions is studied using Monte Carlo simulations and dynamical mean-field approximation. The evolution of the two-dimensional, half-filled system is described by an anisotropic Kawasaki dynamics assuming that the hopping of particles along the principal directions is governed by two heat baths at different temperatures $T_x$ and $T_y$. The system undergoes an order-disorder phase transition as $T_x$ ($T_y$) is varied for sufficiently low fixed $T_y$ ($T_x$). The non-equilibrium phase transition remains continuous and the critical behaviour belongs to the Ising universality class. The measure of violation of the fluctuation-dissipation theorem can be controlled by the value of the fixed temperature. We have found an exponential decay of spatial correlations above the critical region in contrast to the two-temperature model with attractive interactions.