Grain-Boundary Theory of Melting in Two Dimensions

Abstract

A quantitative theory of melting in two dimensions via the spontaneous generation of grain boundaries is presented. It is found that as the temperature is increased, grain boundaries are generated before the dislocations unbind. Also discussed are (a) the nature of the transition, (b) the coupling of the grain boundaries to a density change, (c) the existence of a hexatic phase, and (d) comparisions with recent computer simulations.