Large-Scale Simulations of the Two-Dimensional Melting of Hard Disks

TL;DR

This study uses large-scale simulations of over a million particles to investigate the two-dimensional melting transition of hard disks, providing new insights into the nature of the phase change and correcting previous finite-size artifacts.

Contribution

It offers the first large-scale simulation evidence supporting the Halperin-Nelson-Young theory of 2D melting and refines the melting density estimates.

Findings

Finite-size effects caused the van der Waals loop in smaller simulations.

Results support the Halperin-Nelson-Young theory of two-stage melting.

New lower bound for melting density is significantly higher than previous estimates.

Abstract

Large-scale computer simulations involving more than a million particles have been performed to study the melting transition in a two-dimensional hard disk fluid. The van der Waals loop previously observed in the pressure-density relationship of smaller simulations is shown to be an artifact of finite-size effects. Together with a detailed scaling analysis of the bond orientation order, the new results provide compelling evidence for the Halperin-Nelson-Young picture. Scaling analysis of the translational order also yields a lower bound for the melting density that is much higher than previously thought.