Lattice-gas automata with attractive and repulsive interactions

Particles interacting as square wells or square barriers of finite range r are modeled as a two-dimensional lattice gas, in the spirit of the liquid-gas model of Appert and Zalesky [Phys. Rev. Lett. 64, 1 (1990)]. If r is sufficiently large, the system exhibits phase separation. We derive the equation of state, which is of the van der Waals type. If it has an unstable branch, the Maxwell construction is used. Analytical expressions for the transport coefficients as functions of r are calculated from the decay rates of the hydrodynamic modes. The theoretical results for thermodynamic and transport properties show good agreement with extensive computer simulations