Fluctuations in short-range spin-glasses

Spatial fluctuations in spin-glasses are studied by an expansion to quadratic order around the dynamic mean-field theory. Below Tc, a spatial decay of the "spin-glass susceptibility" [2(R',)]av is characterized at infinitesimal frequencies by a correlation length 3/4() which diverges as the inverse of the time-dependent Edwards-Anderson order parameter q(1) in the limit '0. The Fourier transform of equal-time correlations [S(0')S(R')2]av diverges as k-4, signaling a breakdown of mean-field theory at low T below d=4.