From disordered crystal to glass - Exact theory

Abstract

We calculate thermodynamic properties of a disordered model insulator, starting from the ideal simple-cubic lattice (g = 0) and increasing the disorder parameter g to » 1/2. As in the earlier Einstein and Debye approximations, the ground state energy is discontinuous at gc = 1/2. For g < gc, the low-T heat-capacity C ∼ T3, whereas for g > gc, C ∼ T. The van Hove singularities disappear at any finite magnitude g of the disorder. For g > 1/2 we discover novel fixed points in the self-energy and spectral density of this model glass. © 2001 Elsevier Science B.V. All rights reserved.