A Solvable Model of a Glass

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.