General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
Disordered Systems and Neural Networks
2009-10-31 v1
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.
Keywords
Cite
@article{arxiv.cond-mat/9807333,
title = {General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity},
author = {Stefano Ghirlanda and Francesco Guerra},
journal= {arXiv preprint arXiv:cond-mat/9807333},
year = {2009}
}
Comments
LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical and General. Also available at http://rerumnatura.zool.su.se/stefano/ms/ghigu.ps