A New Look at Low { Temperature Anomalies in

We review a model{based rather than phenomenological approach to low{temperature anomalies in glasses. Speciically, we present a solvable model inspired by spin{glass theory that exhibits both, a glassy low{temperature phase, and a collection of double{ and single{well conngurations in its potential energy landscape. The distribution of parameters characterizing the local potential energy conngurations can be computed, and is found to diier from those assumed in the standard tunneling model and its variants. Still, low temperature anomalies characteristic of amorphous materials are reproduced. More importantly perhaps, we obtain a clue to the universality issue. That is, we are able to distinguish between properties which can be expected to be universal and those which cannot. Our theory also predicts the existence, under suitable circumstances of amorphous phases without low{energy tunneling excitations. Dedicated to Heinz Horner on the occasion of his 60 th birthday.