Critical curves and thermodynamic phases of lattice fluids and antiferromagnets with structured interactions

We study the classical lattice gas with hard cores, nearest-neighbor repulsive forces, and next-nearest-neighbor attractive forces. We find several thermodynamic phases (vapor, liquid, and solid) and unusually shaped critical curves, yet no critical point or triple point. We find and discuss discontinuities in m(h) in the analogous magnetic systems. The principal calculational tool is molecular field theory but accurate numerical solutions of the transfer matrix are also obtained as a check on some of the results. It-is conjectured that the critical line separating vapor and liquid phases (bounded by the triple point on one end and the critical point on the other) exists in the exact solution of a lattice gas with structured, relatively long-ranged interactions, but cannot be found in the molecular field approximation.