One- and three-dimensional lattice models with two repulsive ranges: simple systems with complex phase behaviour

The properties of a simple one-dimensional lattice model with two repulsive ranges (a hard core repulsion that covers two sites and a next-to-nearest neighbour repulsive interaction) and a long-ranged staggered mean field, are studied in terms of its analytic solution. A related three-dimensional lattice model is analysed using computer simulation. Both systems present a phase diagram that displays a disorder-order-disorder transition (or a fluid-solid-fluid transition, in lattice gas language). When the usual mean field attraction is incorporated in the one-dimensional model, the system also exhibits a vapour-liquid transition. The overall appearance of the phase diagram when dispersion forces are included bears some resemblance with the phase diagram of water and related systems.