The solution of the multiscale SK model

We consider a mean field spin system with random interaction in a multiscale thermal equilbrium, namely when the thermodynamic equilibrium is reached through successive hierarchical thermalization. This model apperead in physical literature un the 90's as a possible framework describing thermodynamic properties of systems out of standard Gibbs equilibrium. We show how to construct a variational problem that gives a representation of the thermodynamic limit of the pressure density (generating functional). We present the main ideas behind the proof and discuss possible applications of the result.