Static and dynamic glass-glass transitions: a mean-field study

The behavior of a family of mean-field glass models is reviewed. The models are analyzed by means of a Langevin-based approach to the dynamics and a Replica theory computation of the thermodynamics. We focus on the phase diagram of a particular model case, where glass-to-glass transitions occur between phases with a different number of characteristic time-scales for the relaxation processes. The appearence of Johari-Goldstein processes as collective reorganizations of sets of fast processes is discussed.