From Disordered Crystal to Glass: Exact Theory

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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 earlier Einstein- and Debye- approximations, there is a phase transition 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 g. For g>1/2 we discover novel fixed points in the self-energy and spectral density of this model glass.