Statistical physics of structural glasses

This paper gives an introduction to and brief overview of some of our recent work on the equilibrium thermodynamics of glasses. We have focused on first-principles computations for simple fragile glasses, starting from the two-body interatomic potential. A replica formulation translates this problem into that of a gas of interacting molecules, each molecule being built of m atoms, and having a gyration radius (related to the cage size) which vanishes at zero temperature. We use a small-cage expansion, valid at low temperatures, which allows us to compute the cage size, the specific heat (which follows the Dulong and Petit law), and the configurational entropy. The no-replica interpretation of the computations is also briefly described. The results, particularly those concerning the Kauzmann temperature and the configurational entropy, are compared to recent numerical simulations.