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 ${\mu }_A={\mu }_B=\mu$. The particles interact via on-site 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 $\mu ={\mu }_c$ 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.

38 pages, 16 figures

References in corpus (6)

• Phase behaviour and structure of a superionic liquid in nonpolarized nanoconfinement
• Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior
• The Thermodynamic Transitions of Antiferromagnetic Ising Model on the Fractional Multi-branched Husimi Recursive Lattice
• Exact correlation functions in particle-reaction models with immobile particles
• Binary Reactive Adsorbate on a Random Catalytic Substrate
• Equilibrium properties of two-species reactive lattice gases on random catalytic chains