Computer simulations of the two-dimensional melting transition using hard disks

TL;DR

This paper uses Monte Carlo simulations to study the two-dimensional melting transition of hard disks, providing evidence supporting the KTHNY theory and ruling out first-order or one-stage continuous transitions.

Contribution

The study offers detailed large-scale simulations and finite-size scaling analysis that confirm the KTHNY theory predictions for 2D melting of hard disks.

Findings

Results agree with KTHNY theory predictions.

First-order and one-stage continuous transitions are ruled out.

Critical exponents and transition points are accurately determined.

Abstract

We present detailed Monte Carlo results for the two-dimensional melting transition of various systems up to N=65536 hard disks. The simulations are performed in the NVT ensemble, using a new updating scheme. In the isotropic phase the bond orientational correlation length xi_6 and the susceptibility chi_6 are measured and compared with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. From the scaling relation of xi_6 and chi_6 we calculate the critical exponent eta_6. In the phase transition region we use finite-size scaling methods to locate the disclination binding transition point and compare the results with the values obtained from the behaviour in the isotropic phase. Additionally, we measure the topological defect density, the pressure and the distribution of the second moment of the local bond orientational order parameter. All results are in good agreement with the KTHNY theory, while a first-order phase transition with small correlation length and a one-stage continuous transition can be ruled out.