Large random correlations in individual mean field spin glass samples

Abstract

We argue that complex systems must possess long range correlations and illustrate thisidea on the example of the mean field spin glass model. Defined on the complete graph, thismodel has no genuine concept of distance, but the long range character of correlations istranslated into a broad distribution of the spin–spin correlation coefficients for almost allrealizations of the random couplings. When we sample the whole phase space we find thatthis distribution is indeed so broad that at low temperatures it essentially becomesuniform, with all possible correlation values appearing with the same probability. Thedistribution of correlations inside a single phase space valley is also studied and found to bemuch narrower.