Free energy of bipartite spherical Sherrington-Kirkpatrick model

Abstract

We consider the free energy of the bipartite spherical Sherrington-Kirkpatrick model and determine the limiting free energy at every temperature. We also prove the convergence of the law of the fluctuations of the free energy at non-critical temperature. The limit is given by the Gaussian distribution for all high temperatures and by the GOE Tracy-Widom distribution for all low temperatures. The result is universal and the analysis is applicable to a more general setting including the case where the disorders are non-identically distributed.