Translational Invariance in Models for Low-Temperature Properties of Glasses

We report on a refined version of our spin-glass type approach to the low-temperature physics of structural glasses. Its key idea is based on a Born von Karman expansion of the interaction potential about a set of reference positions in which glassy aspects are modeled by taking the harmonic contribution within this expansion to be random. Within the present refined version the expansion at the harmonic level is reorganized so as to respect the principle of global translational invariance. By implementing this principle, we have for the first time a mechanism that fixes the distribution of the parameters characterizing the local potential energy configurations responsible for glassy low-temperature anomalies solely in terms of assumptions about interactions at a microscopic level.