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 $q=t+t^2+O\left(t^3\right)$ $(t=1-\frac{T}{T_c})$, which differs at $O\left(t^2\right)$ from that given by Sk.