Three-phase point in a binary hard-core lattice model?

TL;DR

This study investigates a two-dimensional binary hard-core lattice model using transfer matrix methods, finding no evidence of a gas-liquid transition and providing insights into its relation with RSOS and Potts models, suggesting a tricritical point.

Contribution

It introduces a transfer matrix analysis of the model, clarifies its phase behavior, and challenges previous Monte Carlo findings of a three-phase point.

Findings

No evidence of a gas-liquid transition was found.

The model is related to a solvable RSOS model with similar exclusion rules.

Analysis supports the presence of a tricritical point rather than a three-phase point.

Abstract

Using Monte Carlo simulation, Van Duijneveldt and Lekkerkerker [Phys. Rev. Lett. 71, 4264 (1993)] found gas-liquid-solid behaviour in a simple two-dimensional lattice model with two types of hard particles. The same model is studied here by means of numerical transfer matrix calculations, focusing on the finite size scaling of the gaps between the largest few eigenvalues. No evidence for a gas-liquid transition is found. We discuss the relation of the model with a solvable RSOS model of which the states obey the same exclusion rules. Finally, a detailed analysis of the relation with the dilute three-state Potts model strongly supports the tricritical point rather than a three-phase point.