Yan V Fyodorov, Jean-Philippe Bouchaud
Published 2008-05-04, updated 2008-08-18Version 2
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. -
Comments: Published version with a few references added, misprints corrected and a few places more clearly written
Journal: J. Phys.A: Math.Theor 41 (2008) 372001 (12pp)
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