Phase diagram of random lattice gases in the annealed limit

TL;DR

This paper analyzes the phase behavior of a random lattice gas in the annealed limit, deriving an exact solution for a model with competing long-range and short-range interactions, revealing complex phase transitions.

Contribution

It provides a detailed analysis and exact solution of a one-dimensional random lattice gas with competing interactions in the annealed limit, highlighting novel phase transition phenomena.

Findings

Presence of three phase transitions at constant temperature

Occurrence of triple and quadruple points

Exact solution for the model with bimodal distribution

Abstract

An analysis of the random lattice gas in the annealed limit is presented. The statistical mechanics of disordered lattice systems is briefly reviewed. For the case of the lattice gas with an arbitrary uniform interaction potential and random short-range interactions the annealed limit is discussed in detail. By identifying and extracting an entropy of mixing term, a correct physical expression for the pressure is explicitly given. As an application, the one-dimensional lattice gas with uniform long-range interactions and random short-range interactions satisfying a bimodal annealed probability distribution is discussed. The model is exactly solved and is shown to present interesting behavior in the presence of competition between interactions, such as the presence of three phase transitions at constant temperature and the occurrence of triple and quadruple points.