# Liquid-Hextic-Solid Phase Transition of a Hard-Core Lattice Gas with Third Neighbor Exclusion

## TL;DR

This paper investigates the phase transitions in a two-dimensional hard-core lattice gas with third neighbor exclusion, revealing a two-step liquid-hexatic-solid transition through a novel kinetic approach and visualization techniques.

## Contribution

It introduces an alternative kinetic method based on the Gibbs adsorption isotherm and random sequential adsorption with surface diffusion to analyze phase behavior.

## Key findings

- First-order phase transition confirmed at high surface coverage.
- Two-step liquid-hexatic-solid transition observed.
- Visualization of local bond orientation supports phase identification.

## Abstract

The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by use of the random sequential adsorption with surface diffusion (RSAD) model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage.