Effective temperatures in an exactly solvable model for a fragile glass

A model glass with facilitated dynamics is considered with one type of fast process (beta type) and one type of slow process (alpha type). On time scales where the fast processes are in equilibrium, the slow ones have a dynamics that resembles that of facilitated spin models. The main features are the occurrence of a Kauzmann transition, a Vogel-Fulcher-Tammann-Hesse behavior for the relaxation time, an Adam-Gibbs relation between relaxation time and configurational entropy, and an aging regime. The model is such that its statics is simple and its (Monte Carlo type) dynamics is exactly solvable. The dynamics has been studied both on the approach to the Kauzmann transition and below it. In certain parameter regimes it is so slow that a quasiequilibrium occurs at a time dependent effective temperature. Correlation and response functions are also computed, as well as the out of equilibrium fluctuation-dissipation relation, showing the uniqueness of the effective temperature, thus giving support to the rephrasing of the problem within the framework of out of equilibrium thermodynamics.