Stable and metastable states in mean-field Potts and structural glasses

Recent static and dynamical work suggest a close analogy between spin glasses with discontinuous Edwards-Anderson order parameter and structural glasses. The mean-field dynamical spin-glass theory predicts freezing above the usual thermodynamic transition temperature. Here we use the approach of Thouless, Anderson, and Palmer for Potts glasses to show that the dynamical approach locates a thermodynamically metastable glassy state. We also give divergent correlation lengths as both the static and dynamical transition temperatures are approached. We argue that the static transition is analogous to an ideal glass transition temperature in the structural glass problem. We also argue that the static transition temperature can be identified as the temperature at which the configurational entropy vanishes, i.e., the Kauzmann temperature. Dynamical transitions between the metastable states are discussed. We argue that divergent lifetimes occur near the Kauzmann temperature.