Gauge theory of defect melting-status 1984

Abstract

We show that the grand-canonical ensemble of line-like defects in crystals can be described by a gauge theory of theGinzburg-Landau type which normally governs the magnetic phenomena in superconductors. We use this theory to study the melting transition. It leads to a close structural correspondence between superconductive and crystalline properties. The vector potential of magnetism and the order parameter correspond to the potential of stress and the disorder parameter, respectively. The Meissner effect which prevents magnetism from invading the ordered state of a superconductor corresponds to the screening of stress in the disordered molten state. There is however, an important difference which causes melting to be a first order transition: It is the presence of two types of disorder fields, one for dislocations and one for disclinations with different long-range interactions. The melting process is the result of a combined proliferation of both types of defects. We exhibit the important backfeeding mechanism which is responsible for the first order of the transition. The theoretical ideas are exemplified by a simple statistical model, similar to the XY model of magnetism, which isdually equivalent to an ensemble of crystalline defects including their long-range stress interactions. Since it is a local model with next-neighbour coupling it can be simulated on a computer and shows a proper first order melting transition.