Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential
Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential
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DOI：
10.1088/1751-8113/41/37/372001
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发表时间：
2008-09-19
影响因子：
2.1
通讯作者：
Bouchaud, Jean-Philippe
中科院分区：
文献类型：
--
作者：
Fyodorov, Yan V.;Bouchaud, Jean-Philippe
本文研究了Carpentier和Le Doussal（CLD）提出的随机能量模型（REM）的冻结情景对随机势相互关联的影响。我们介绍了一个特定的（圆形）的模型的变体，并表明，在高温阶段的配分函数的整数矩是由著名的戴森库仑气体积分。CLD冻结方案允许人们使用这些时刻提取在高温和低温阶段的自由能分布。特别是，它产生的潜力序列中的最小值的全分布。这为强相关变量提供了一个明确的新的极值统计类，明显不同于标准的Gumbel类。
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.