The freezing phase transition in hard core lattice gases on triangular lattice with exclusion up to seventh next-nearest neighbor

TL;DR

This study investigates phase transitions in hard core lattice gases on a triangular lattice with exclusion up to the seventh neighbor, revealing discontinuous transitions and providing precise critical parameters.

Contribution

It extends previous work to higher exclusion ranges ($k extless=7$) using advanced algorithms, uncovering the nature of phase transitions in these models.

Findings

Discontinuous phase transitions for $4 extless= k extless=7$

Accurate determination of critical chemical potential and coexistence densities

Identification of a single transition from fluid to sublattice-ordered phase

Abstract

Hard core lattice gas models are minimal models to study entropy driven phase transitions. In the $k$-NN lattice gas, a particle excludes all sites upto the $k$-th next-nearest neighbors from being occupied by another particle. As $k$ increases from one, it extrapolates from nearest neighbor exclusion to the hard sphere gas. In this paper, we study the model on the triangular lattice for $k\leq 7$ using a flat histogram algorithm that includes cluster moves. Earlier studies had focused on $k\leq 3$. We show that for $4\leq k\leq 7$, the system undergoes a single phase transition from a low-density fluid phase to a high-density sublattice-ordered phase. Using partition function zeros and non-convexity properties of the entropy, we show that the transitions are discontinuous. The critical chemical potential, coexistence densities, and critical pressure are determined accurately.