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General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity

Stefano Ghirlanda·Francesco Guerra
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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.

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Stefano Ghirlanda, Francesco Guerra. 1998-07-24. General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity. https://doi.org/10.1088/0305-4470%2F31%2F46%2F006

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