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

TL;DR

This paper provides exact phase diagrams for a binary lattice-gas model with soft exclusion interactions on tree-like lattices, revealing critical behaviors and phase transitions including symmetry breaking and re-entrant phenomena.

Contribution

It offers the first exact analysis of phase diagrams for binary lattice-gases with soft exclusion on Bethe and Husimi lattices, highlighting the effects of interaction strength on phase transitions.

Findings

Identified critical points and phase boundaries for different interaction strengths.

Discovered continuous and first-order phase transitions depending on interaction parameters.

Showed differences in ordering phenomena between Bethe and Husimi lattices due to frustration.

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.