FAST TRACK COMMUNICATION: Freezing and extremevalue 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 hightemperature phase are given by the wellknown 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 lowtemperature phases. In particular, it yields the full distribution of the minimal value in the potential sequence. This provides an explicit new class of extremevalue statistics for strongly correlated variables, manifestly different from the standard Gumbel class.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 September 2008
 DOI:
 10.1088/17518113/41/37/372001
 arXiv:
 arXiv:0805.0407
 Bibcode:
 2008JPhA...41K2001F
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 Published version with a few references added, misprints corrected and a few places more clearly written