Abstract

We review calculations leading to the conclusion that, thermally excited dislocation loops in a three dimensional bulk elastic solid may drive a mechanical instability in which the shear modulus vanishes. This vanishing follows a power law as a function of temperature, typical of a second order phase transition. The exponent is universal in the sense that it does not, depend on the values taken by the microscopic parameters of the model: Burgers vector, lattice constant, elastic constants in the absence of dislocations, and dislocation core structure. The basic calculations follow a scale dependent, effective medium approach first proposed by Kosterlitz and Thouless in two dimensions. An instability arises because loops of widely different sizes may be excited, and large ones facilitate the creation of small ones, which in turn screen the self energy of the large ones. Ideas and methods are illustrated with two simplified, but interesting in their own right, models: one is the lambda, transition in superfiuid Helium, in which vortex loops driven an instability that causes the superfiuid density to vanish. Another is the mechanical instability driven by dislocation dipoles in two dimensions. Along the way, brief overviews of the current status of two dimensional melting and of the superheating of bulk solids are given.