Theory of the phase transition from a disordered cubic crystal to a glass

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 $\gg 1/2$. As in the earlier Einstein- and Debye- approximations, the ground state energy is discontinuous at $g_{c} = 1/2$. For $g<g_{c}$ the low-T heat-capacity $C \sim T^{3}$ whereas for $g>g_{c}$, $C \sim T$. The van Hove singularities disappear at {\em any} finite magnitude $g$ of the disorder. For $g>1/2$ we discover novel {\em fixed points} in the self-energy and spectral density of this model glass.