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

Submitted to Phys. Rev. Lett., 8 pages, 4 figures