Monte Carlo simulations of 2d hard core lattice gases

TL;DR

This study uses Monte Carlo simulations to analyze phase transitions in 2D lattice gases with varying exclusion ranges, revealing unexpected universality classes and transition types that challenge existing theoretical predictions.

Contribution

It provides new insights into the critical behavior of lattice gases with extended exclusions, especially highlighting discrepancies with Landau-Lifshitz theory.

Findings

1NN exclusion undergoes a continuous Ising transition.

2NN exclusion also exhibits a continuous Ising transition.

3NN exclusion results in a discontinuous transition.

Abstract

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, $\lambda$ (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class -- contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.