  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.

Statistical Mechanics;Disordered Systems and Neural Networks