Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly

TL;DR

This study uses transfer matrix and finite-size scaling methods to analyze a two-particle lattice gas model, revealing phase transitions, density anomalies, and universality classes related to the Ising and tricritical Ising models.

Contribution

It introduces a detailed analysis of athermal lattice gas with two particle types, identifying phase behavior and critical properties using transfer matrix techniques.

Findings

Identified disordered and ordered phases with a phase transition.

Discovered a tricritical point separating continuous and discontinuous transitions.

Observed density minima in isobaric curves indicating density anomaly.

Abstract

Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.