Some observations on the mean-field theory of spin glasses

Abstract

A finite negative ground state energy and a non-negative ground state entropy appear to be incompatible unless linear response theory is abandoned in the spin glass phase. Various approaches using the method of broken replica symmetry are discussed. The symmetry-breaking scheme used previously by the authors is generalised to the case of an asymmetric bond distribution and the existence of a new phase, between the ferromagnetic and spin glass phases is noted. For a symmetric bond distribution it is observed that the failure of the Fischer relation chi = beta (1-q) seems to be a general consequence of replica symmetry-breaking. A physical argument for this is given, based on the hypothesis that linear response theory breaks down in the spin glass phase because of the quasi-degeneracy of the spin glass ordering.