Replica-Symmetry Breaking in Spin-Glass Theories

Abstract

The instability which arises in current mean-field theories of spin-glasses is removed, within the replica method, by breaking the symmetry between replicas. For the Sherrington-Kirkpatrick (SK) model the spin-glass order parameter has the expansion $q=t+{t}^{2}+O({t}^{3})$ $(t=1\ensuremath{-}\frac{T}{{T}_{c}})$, which differs at $O({t}^{2})$ from that given by Sk.