Universality in the Three-Dimensional Hard-Sphere Lattice Gas

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the three-dimensional hard-sphere lattice gas, revealing it does not belong to the Ising universality class, with specific critical exponents measured.

Contribution

It provides the first detailed critical exponent measurements for the 3D hard-sphere lattice gas, challenging its classification within the Ising universality class.

Findings

Critical exponents $eta/ u$ and $\gamma/ u$ measured

Hard-sphere lattice gas differs from 3D Ising model

Supports non-Ising universality class in 3D

Abstract

We perform Monte Carlo simulations of the hard-sphere lattice gas on the body-centred cubic lattice with nearest neighbour exclusion. We get the critical exponents, $\beta/\nu = 0.311(8)$ and $\gamma/\nu = 2.38(2)$, where $\beta$, $\gamma$, and $\nu$ are the critical exponents of the staggered density, the staggered compressibility, and the correlation length, respectively. The values of the hard-sphere lattice gas on the simple cubic lattice agree with them but those of the three-dimensional Ising model do not. This supports that the hard-sphere lattice gas does not fall into the Ising universality class in three dimensions.