Yan V Fyodorov and Jean-Philippe Bouchaud 2008 J. Phys. A: Math. Theor. 41 372001 doi:10.1088/1751-8113/41/37/372001
Yan V Fyodorov1 and Jean-Philippe Bouchaud2
Show affiliationsWe 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.
05.70.Ce Thermodynamic functions and equations of state
Issue 37 (19 September 2008)
Received 28 May 2008, in final form 19 July 2008
Published 7 August 2008
Yan V Fyodorov and Jean-Philippe Bouchaud 2008 J. Phys. A: Math. Theor. 41 372001
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