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arXiv · 0805.0407

Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential

Yan V Fyodorov·Jean-Philippe Bouchaud
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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. -

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Yan V Fyodorov, Jean-Philippe Bouchaud. 2008-08-18. Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential. https://doi.org/10.1088/1751-8113%2F41%2F37%2F372001

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