General Properties of Overlap Probability Distributions in Disordered Spin Systems. toward Parisi Ultrametricity
نویسندگان
چکیده
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 as+1 between one of the rst 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 ab , with b running among the rst s replicas, excluding a. Each of these cases has equal probability 1=s.
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