Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential

被引:123
作者
Fyodorov, Yan V. [1 ]
Bouchaud, Jean-Philippe [2 ]
机构
[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England
[2] Sci & Finance, F-75009 Paris, France
关键词
D O I
10.1088/1751-8113/41/37/372001
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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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页数:12
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