  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.
