First order phase transitions in classical lattice gas spin models

TL;DR

This paper investigates first order phase transitions in classical lattice gas models with multi-component spins on 2D and 3D lattices, using Monte Carlo simulations to explore the effects of negative chemical potential.

Contribution

It provides new simulation-based evidence of first order transitions in lattice gas models at negative chemical potentials, extending previous mean field and Monte Carlo studies.

Findings

Evidence of first order phase transitions at negative chemical potential.

Quantitative characterization of transition behavior in 2D and 3D models.

Comparison with recent experimental results supports the simulation findings.

Abstract

The present paper considers some classical ferromagnetic lattice--gas models, consisting of particles that carry $n$--component spins ($n=2,3$) and associated with a $D$--dimensional lattice ($D=2,3$); 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 site occupation is also controlled by the chemical potential $\mu$. The models had previously been investigated by Mean Field and Two--Site Cluster treatments (when D=3), as well as Grand--Canonical Monte Carlo simulation in the case $\mu=0$, for both D=2 and D=3; the obtained results showed the same kind of critical behaviour as the one known for their saturated lattice counterparts, corresponding to one particle per site. Here we addressed by Grand--Canonical Monte Carlo simulation the case where the chemical potential is negative and sufficiently large in magnitude; the value $\mu=-D/2$ was chosen for each of the four previously investigated counterparts, together with $\mu=-3D/4$ in an additional instance. We mostly found evidence of first order transitions, both for D=2 and D=3, and quantitatively characterized their behaviour. Comparisons are also made with recent experimental results.