Non-equilibrium Relaxation Analysis on Two-dimensional Melting

TL;DR

This study investigates the two-dimensional melting transition in a hard-disk system using non-equilibrium relaxation analysis, identifying the critical point and critical exponent consistent with theoretical predictions.

Contribution

It applies non-equilibrium relaxation analysis to determine the critical point and exponent in 2D melting, providing empirical validation of theoretical models.

Findings

Critical point between hexatic and fluid phases identified

Critical exponent η estimated as 0.25(2)

Results consistent with Kosterlitz-Thouless-Halperin-Nelson-Young theory

Abstract

The melting transition in the hard-disk system is considered. Non-equilibrium relaxation analysis of the six-fold bond-orientational order parameter has been carried out. The critical point between the hexatic and the fluid phase is determined on the basis of the dynamic scaling hypothesis. The value of the critical exponent $\eta$ is determined from the fluctuation of the order parameter at the criticality as $\eta = 0.25(2)$ which is consistent with the prediction by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.