On spin glass fluctuations

Abstract

We compute the bare correlation function < Qαβ p Qαβ-p> for the short range spin glass, around Parisi mean field solution, in field near Tc. We evaluate both the correlation function associated with a given overlap x (of replicas α, β) and the x-average i.e. the Fourier transform of the spin correlation < σi σj >2, (p conjugate to |i - j|). In field the dominant infrared behaviour is in p-3 in all cases. In zero field it is in p-4, p- 3, p-3 In p respectively for x ≤ p, p ≤ x and the statistical mechanics average, agreeing in the first instance with the dynamic (x = 0) result of Sompolinsky Zippelius