Berezinskii-Kosterlitz-Thouless transition in two-dimensional lattice gas models

TL;DR

This study investigates the Berezinskii-Kosterlitz-Thouless transition in two-dimensional lattice-gas models with multicomponent magnetic particles, revealing how vacancies lower the transition temperature compared to saturated lattice models.

Contribution

It introduces a lattice-gas model with vacancies and analyzes its critical behavior, demonstrating the occurrence of a BKT transition influenced by fluid-like observables.

Findings

BKT transition observed in the lattice-gas model

Transition temperature is lower than in saturated models

Vacancies influence critical behavior

Abstract

We have considered two classical lattice-gas models, consisting of particles that carry multicomponent magnetic momenta, and associated with a two-dimensional square lattices; each site can host one particle at most, thus implicitly allowing for hard-core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic and involves only two components. The case of zero chemical potential has been investigated by Grand--Canonical Monte Carlo simulations; the fluctuating occupation numbers now give rise to additional fluid-like observables in comparison with the usual saturated--lattice situation; these were investigated and their possible influence on the critical behaviour was discussed. Our results show that the present model supports a Berezinskii-Kosterlitz-Thouless phase transition with a transition temperature lower than that of the saturated lattice counterpart due to the presence of ``vacancies''; comparisons were also made with similar models studied in the literature.