Ergodicity of the Coupling Constants and the Symmetricn-Replicas Trick for a Class of Mean-Field Spin-Glass Models

A large class of mean-field spin-glass models is solved by two methods. The first one uses an ergodicity hypothesis for the random variables which enter in the definition of the coupling constants. The second method is the well-known $n$-replicas trick. The comparison of these two methods when applied to a limit Hamiltonian of the class gives new insights on the Sherrington-Kirkpatrick model and on the breaking of the replicas' symmetry.