AN INVESTIGATION OF THE HIDDEN STRUCTURE OF STATES IN A MEAN-FIELD SPIN-GLASS MODEL

We study the geometrical structure of the states in the low-temperatur e phase of a mean-field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard me thods, mainly due to the presence of an exponentially high number of s tates, each one having a vanishing weight in the thermodynamic limit. Performing a purely entropic computation, based on the TAP equations f or this model, we define a constrained complexity which gives the over lap distribution of the states. We find that this distribution is cont inuous, non-random and highly dependent on the energy range of the con sidered states. Furthermore, we show which is the geometrical shape of the threshold landscape, giving some insight into the role played by threshold states in the dynamical behaviour of the system.