Comparison between dynamical theories and metastable states in regular and glassy mean-field spin models with underlying first-order-like phase transitions

A comparison of dynamical theories and metastable states in regular and glassy (mean-field) spin models with underlying first-order-like phase transitions is made. We emphasize that for the glassy case, fluctuations probe the region in phase space where metastable states exist. This is contrasted to the situation for regular spin models. We physically interpret our results in terms of a dynamical instability of the paramagnetic phase in the glassy models. For the glassy case we conclude that as soon as metastable states exist, the mean-field model exhibits an ergodic to nonergodic transition where full ensemble averages are no longer equal to time averages.