The replica-symmetry-breaking solution of the Hopfield model at zero temperature: Critical storage capacity and frozen field distribution

Abstract

The full replica-symmetry-breaking (RSB) solution of the Hopfield model at zero temperature (T=0) is investigated. By using the RSB scheme by de Dominicis, Gabay and Orland, a free-energy functional in the so-called Sompolinsky gauge and variational equations are formulated. The resulting equations are conveniently defined for numerical analysis since a singularity at T=0 is formally avoided. Elaborate numerical analyses provide a corrected storage capacity, order parameter functions and the frozen field distribution both in the spin-glass phase and the ferromagnetic retrieval phase.