Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods

TL;DR

This study uses three simulation methods to investigate the melting transition in hard-disk systems, confirming a first-order phase transition and the existence of a hexatic phase in two dimensions.

Contribution

It provides a comparative analysis of simulation techniques and confirms the first-order melting transition with detailed phase coexistence visualization.

Findings

Confirmation of first-order melting transition in hard disks

Visualization of phase coexistence via orientational order

Verification of the hexatic phase presence

Abstract

We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.