Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential
Abstract
We investigate some implications of the freezing scenario proposed by Carpentier and Le Doussal (CLD) for a random energy model (REM) with logarithmically correlated random potential. We introduce a particular (circular) variant of the model, and show that the integer moments of the partition function in the high-temperature phase are given by the well-known Dyson Coulomb gas integrals. The CLD freezing scenario allows one to use those moments for extracting the distribution of the free energy in both high- and low-temperature phases. In particular, it yields the full distribution of the minimal value in the potential sequence. This provides an explicit new class of extreme-value statistics for strongly correlated variables, manifestly different from the standard Gumbel class. -
Cite
@article{arxiv.0805.0407,
title = {Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential},
author = {Yan V Fyodorov and Jean-Philippe Bouchaud},
journal= {arXiv preprint arXiv:0805.0407},
year = {2009}
}
Comments
Published version with a few references added, misprints corrected and a few places more clearly written