Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas

TL;DR

This study uses Monte Carlo simulations to analyze the hard-sphere lattice gas on a simple cubic lattice, estimating critical activity and concluding the absence of re-entrant phase transitions in the related antiferromagnetic Ising model.

Contribution

It provides the first Monte Carlo estimate of the critical activity for the hard-sphere lattice gas on the simple cubic lattice and clarifies the phase transition behavior of the related Ising model.

Findings

Critical activity estimated as z_c = 1.0588 ± 0.0003

No re-entrant phase transition observed in the antiferromagnetic Ising model

Monte Carlo simulations confirm theoretical predictions

Abstract

We perform the Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, $z_{\rm c} = 1.0588 \pm 0.0003$. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice.