Characterization of the Melting Transition in Two Dimensions at Vanishing External Pressure Using Molecular Dynamics Simulations

TL;DR

This molecular dynamics study investigates the melting transition in a two-dimensional Lennard-Jones particle system at zero external pressure, examining dislocation behavior, elastic constants, and the nature of the phase transition.

Contribution

It provides detailed simulation evidence on the melting process in 2D, analyzing dislocation proliferation, elastic constants, and the absence of a stable hexatic phase near melting.

Findings

Dislocation pairs proliferate near melting temperature.

Elastic constant approaches KTHNY theory prediction.

No stable hexatic phase observed in simulations.

Abstract

A molecular dynamics study of a two dimensional system of particles interacting through a Lennard-Jones pairwise potential is performed at fixed temperature and vanishing external pressure. As the temperature is increased, a solid-to-liquid transition occurs. When the melting temperature $T_c$ is approached from below, there is a proliferation of dislocation pairs and the elastic constant approaches the value predicted by the KTHNY theory. In addition, as $T_c$ is approached from above, the relaxation time increases, consistent with an approach to criticality. However, simulations fail to produce a stable hexatic phase using systems with up to 90,000 particles. A significant jump in enthalpy at $T_c$ is observed, consistent with either a first order or a continuous transition. The role of external pressure is discussed.