# Estimating the Critical Parameters of the Hard Square Lattice Gas Model

## TL;DR

This paper estimates the critical activity of the hard square lattice gas model using an approximation scheme that considers defects and overhangs, achieving results close to Monte Carlo simulations.

## Contribution

It introduces a novel approximation method to estimate the critical activity, improving accuracy over previous estimates.

## Key findings

- Estimated critical activity $z_c=105.35$
- Good agreement with Monte Carlo result $z_c \\approx 97.5$
- Improves upon earlier estimates of $z_c$

## Abstract

The hard square lattice gas model on a square lattice is known to undergo a continuous phase transition from a low density fluid-like phase to high density phase with columnar or smectic order. We estimate the critical activity $z_c$ by calculating, within an approximation scheme, the interfacial tension between two differently ordered columnar phases, and then setting it to zero. The approximation scheme allows for the ordered phases to have multiple defects and the interface between the ordered phases to have overhangs. We estimate $z_c=105.35$, which is in good agreement with existing Monte Carlo simulation results of $z_c \approx 97.5$, and is an improvement over earlier best estimates of $z_c=54.87$ and $z_c=135.63$.