Complexity in mean-field spin-glasses

We look at recent important improvements in the comprehension of the properties of mean-field magnetic models with built-in quenched disorder, qualitatively well describing both the spin-glass and the glass phase. Connecting apparently different approaches, we present our results on a particular model displaying both a glass and a spin-glass phase in different regions of the thermodynamic parameters space, focusing on the complexity function counting the number of relevant stable and metastable states.