Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices

Abstract

We study equilibrium properties of binary lattice-gases comprising A and B particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials µ A = µ B = µ. The particles interact via onsite hard-core exclusion and also between the nearest-neighbours: there are a soft repulsion for AB pairs and interactions of arbitrary strength J, positive or negative, for AA and BB pairs. For tree-like Bethe and Husimi lattices we determine the full phase diagram of such a ternary mixture of particles and voids. We show that for J being above a lattice-dependent threshold value, the critical behaviour is similar: the system undergoes a transition at µ = µ c from a phase with equal mean densities of species into a phase with a spontaneously broken symmetry, in which the mean densities are no longer equal. Depending on the value of J, this transition can be either continuous or of the first order. For sufficiently big negative J, the behaviour on the two lattices becomes markedly different: while for the Bethe lattice there exists a continuous transition into a phase with an alternating order followed by a continuous re-entrant transition into a disordered phase, an alternating order phase is absent on the Husimi lattice due to strong frustration effects.