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

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

1998-07-24

arxiv.org/abs/cond-mat/9807333v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical and General. Also available at http://rerumnatura.zool.su

Scientific paper

10.1088/0305-4470/31/46/006

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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