Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?

TL;DR

This study uses advanced Monte Carlo simulations to clarify the phase transition behavior of a specific lattice gas model, revealing only one first-order transition and no hexatic phase as previously suggested.

Contribution

It provides the first definitive numerical evidence that the model exhibits a single first-order phase transition, contradicting earlier claims of two transitions and a hexatic phase.

Findings

Only one phase transition observed, from fluid to ordered phase.

Transition is first order, with accurately determined critical parameters.

Hexatic phase is absent in the system.

Abstract

We obtain the phase diagram of the hard core lattice gas with third nearest neighbor exclusion on the triangular lattice using Monte Carlo simulations that are based on a rejection-free flat histogram algorithm. In a recent paper [J. Chem. Phys. 151, 104702 (2019)], it was claimed that the lattice gas with third nearest neighbor exclusion undergoes two phase transitions with increasing density, with the phase at intermediate densities exhibiting hexatic order with continuously varying exponents. Though a hexatic phase is expected when the exclusion range is large, it has not been seen earlier in hard core lattice gases with short range exclusion. In this paper, by numerically determining the entropies for all densities, we show unambiguously that there is only a single phase transition in the system between a low-density fluid phase and a high-density ordered sublattice phase, and that a hexatic phase is absent. The transition is shown to be first order in nature and the critical parameters are determined accurately.