Internal field distribution in the infinite-range Ising spin glass

Abstract

The authors have studied the internal field distribution P(H) in the infinite-range Ising spin glass within the framework of the replica method. Their results show that breaking of replica symmetry in the spin-glass phase yields a non-gaussian internal field distribution. Using Parisi's scheme for symmetry breaking they derive a set of Fokker-Planck-like differential equations that are obeyed by both P(H) and the multiple correlation functions in replica space. For t=1-T/Tc<<1 the equations can be integrated perturbatively and the field distribution thus obtained deviates from a guassian form, exhibiting a second maximum which increases and moves toward the origin as t increases. The asymmetry factor for P(H) is shown to be negative and of the order of t5.