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

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.

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

References in corpus (2)

• About the overlap distribution in mean field spin glass models
• 3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

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