Dynamics within metastable states in a mean-field spin glass

In this letter we present a dynamical study of the structure of metastable states (corresponding to TAP solutions) in a mean-field spin-glass model. After reviewing known results of the statical approach, we use dynamics: starting from an initial condition thermalized at a temperature between the statical and the dynamical transition temperatures, we are able to study the relaxational dynamics within metastable states and we show that they are characterized by a true breaking of ergodicity and exponential relaxation.