Orientational order and solid-liquid coexistence in the two-dimensional Lennard-Jones system

Abstract

There exist large discrepancies between the results of different techniques used to locate the melting point of a two-dimensional Lennard-Jones system. In particular, the melting line determined by Barker et al [Physica 106A, 226 (1981)] through thermodynamic integration differs from the limit of mechanical stability of the two-dimensional (2D) solid which follows from recent simulations on very large systems. This discrepancy is puzzling because in the latter simulations no hysteresis was observed. We report a new calculation of the relevant part of the melting line of a 2D Lennard-Jones system by thermodynamic integration. Our results differ significantly from the results reported by Barker et al. and agree well with the simulations on large systems. We note that the structural properties of the two-phase region for a large system [O(104) particles] exhibit all the characteristics of a bond-orientational order-disorder transition. This suggests that solid-liquid coexistence in 2D may differ qualitatively from its three-dimensional counterpart.