Direct test of defect mediated laser induced melting theory for two dimensional solids

TL;DR

This study tests a dislocation unbinding theory for laser-induced melting in 2D solids by solving flow equations with parameters from Monte Carlo simulations, finding good agreement for hard disks and some discrepancies for soft potentials.

Contribution

It provides a direct numerical validation of a dislocation-based melting theory for two-dimensional systems, emphasizing the importance of higher-order defect contributions.

Findings

Flow equations need third-order defect fugacity accuracy.

Excellent agreement with Monte Carlo for hard disks.

Quantitative discrepancies for soft potentials explained.

Abstract

We investigate by direct numerical solution of appropriate renormalization flow equations, the validity of a recent dislocation unbinding theory for laser induced freezing/melting in two dimensions. The bare elastic moduli and dislocation fugacities which are inputs to the flow equations are obtained for three different 2-d systems (hard disk, inverse $12^{th}$ power and the Derjaguin-Landau-Verwey-Overbeek potentials) from a restricted Monte Carlo simulation sampling only configurations {\em without} dislocations. We conclude that (a) the flow equations need to be correct at least up to third order in defect fugacity to reproduce meaningful results, (b) there is excellent quantitative agreement between our results and earlier conventional Monte Carlo simulations for the hard disk system and (c) while the qualitative form of the phase diagram is reproduced for systems with soft potentials there is some quantitative discrepancy which we explain.