Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles

TL;DR

This paper models a mixed lattice gas with two particle sizes on a Bethe lattice, revealing complex phase transitions including continuous, discontinuous, and reentrant behaviors influenced by particle activities.

Contribution

It provides an exact solution for a two-particle-type lattice gas with excluded volume interactions on a Bethe lattice, highlighting phase transition types and reentrant phenomena.

Findings

Identifies a tricritical point separating continuous and discontinuous transitions.

Reveals reentrant fluid-solid transition behavior at low small-particle density.

Shows the phase diagram features a minimum in total density as a function of particle activities.

Abstract

Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which occupy one site and its first neighbors. We solve the model on a Bethe lattice of arbitrary coordination number $q$. In the parameter space defined by the activities of both particles. At low values of the activity of small particles ($z_1$) we find a continuous transition from the fluid to the solid phase as the activity of large particles ($z_2$) is increased. At higher values of $z_1$ the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at $z_1=0$ and displays a minimum before reaching the tricritical point, so that a reentrant behavior is observed for constant values of $z_2$ in the region of low density of small particles. The isobaric curves of the total density of particles as a function of $z_1$ (or $z_2$) show a minimum in the fluid phase.