Orientational order of the two-dimensional hard disk system

TL;DR

This study uses Monte Carlo simulations to analyze the orientational order in a two-dimensional hard disk system, providing evidence for a continuous phase transition consistent with Kosterlitz-Thouless-Halperin-Nelson-Young theory.

Contribution

Introduces a new updating scheme for large-scale Monte Carlo simulations and analyzes bond orientational order to clarify the nature of the phase transition.

Findings

Data support a continuous transition as predicted by KT-HN-Y theory.

First-order transition is unlikely based on the scaling behavior.

Bond orientational order parameter analysis aligns with theoretical predictions.

Abstract

We report Monte Carlo results for the two-dimensional hard disk system. Simulations were performed in the NVT ensemble with up to 65536 disks, using a new updating scheme. We analyze the bond orientational order parameter and correlation length in the isotropic phase and the scaling behaviour of the bond orientational order parameter in the transition region. The data are consistent with predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory, while a first-order phase transition is unlikely and a one-stage continuous transition can be ruled out.