Geometrical Quasiparticle Condensation Model of Melting in Two Dimensions

Abstract

In this paper we describe a new model of the two-dimensional (2D) melting transition, motivated by the recent observation of Glaser and Clark that the structure of a 2D simple dense liquid can be characterized as a random square-triangle tiling containing numerous low-strength tiling faults. The model is based on the assumption that melting is associated with the proliferation and condensation of geometrical quasiparticles, which in 2D are local, nontopological fluctuations from the triangular crystal lattice to the square lattice. The quasiparticles interact via strong, highly anisotropic, short-ranged interactions that produce the characteristic tiling structure of the 2D liquid. This model is derived from and illustrated by molecular dynamics simulation studies of 2D liquid structure, and quantified using a lattice representation that embodies its essential features. The model exhibits a first-order transition for sufficiently strong quasiparticle interactions, and accounts for the volume change associated with melting in a straightforward way. However, there is no phase transition as a function of temperature for the choice of quasiparticle interactions that most accurately reproduces the local geometry of the 2D liquid, suggesting that the contribution of topological defects to the thermodynamics of the melting transition cannot be neglected.