- 98-540 Stefano Ghirlanda and Francesco Guerra
- General properties of overlap probability distributions in
disordered spin systems. Toward Parisi ultrametricity.
(24K, LaTeX 2e)
Jul 24, 98
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Abstract. For a very general class of probability distributions in disordered
Ising spin systems, in the thermodynamical limit, we prove the following
property for overlaps among real replicas. Consider the overlaps among s
replicas. Add one replica s+1. Then, the overlap q(a,s+1) between one of
the first s replicas, let us say a, and the added s+1 is either independent
of the former ones, or it is identical to one of the overlaps q(a,b),
with b running among the first s replicas, excluding a. Each of these
cases has equal probability 1/s.