Simulation of melting of two dimensional Lennard-Jones solids

TL;DR

This study uses large-scale Monte Carlo simulations to investigate the two-stage melting process of a 2D Lennard-Jones solid, providing numerical evidence supporting the KTHNY theory with detailed analysis of order parameters and critical exponents.

Contribution

It offers the first large-scale simulation evidence confirming the two-stage melting scenario in 2D Lennard-Jones solids, including detailed critical behavior analysis.

Findings

Support for two-stage melting with hexatic phase

Different temperature dependence of correlation lengths

Critical exponents consistent with KTHNY theory

Abstract

We study the nature of melting of a two dimensional (2D) Lennard-Jones solid using large scale Monte Carlo simulation. We use systems of up to 102,400 particles to capture the decay of the correlation functions associated with translational order (TO) as well as the bond-orientational (BO) order. We study the role of dislocations and disclinations and their distribution functions. We computed the temperature dependence of the second moment of the two order parameters, i.e., of the TO order parameter as well as of the order parameter associated with BO order and using finite-size scaling we determined the corresponding two anomalous dimension critical exponents eta. We also computed the temperature dependent distribution of these two order parameters on the complex plane which support a two stage melting with a hexatic phase as an intermediate phase. The analysis of our results leads to a consistent picture strongly supporting a two stage melting scenario as predicted by the Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY) theory. We find that the two correlation lengths associated with translational and bond-orientational order have a distinctly different temperature dependence each diverging at different temperature and that their finite size scaling properties are consistent with the KTHNY theory. We also used the temperature dependence of etas and their theoretical bounds to provide estimates for the two critical temperatures, which are found to be in agreement with those determined from the divergent correlation lengths and from the Binder ratio.