A solvable model of a glass

Abstract

An analytically tractable model is introduced which exhibits both, a glass-like freezing transition, and a collection of double-well configurations in its zero-temperature potential energy landscape. The latter are generally believed to be responsible for the anomalous low-temperature properties of glass-like and amorphous systems via a tunneling mechanism that allows particles to move back and forth between adjacent potential energy minima. Using mean-field and replica methods, we are able to compute the distribution of asymmetries and barrier-heights of the double-well configurations analytically, and thereby check various assumptions of the standard tunneling model. We find, in particular, strong correlations between asymmetries and barrier-heights as well as a collection of single-well configurations in the potential energy landscape of the glass-forming system — in contrast to the assumptions of the standard model. Nevertheless, the specific heat scales linearly with temperature over a wide range of low temperatures.

supported by a Heisenberg fellowship