Microcanonical Analysis of the Random Energy Model in a Random Magnetic Field

被引：0

作者：

Louis-Pierre Arguin

Nicola Kistler

机构：

[1] Université de Montréal,Département de Mathématiques et Statistique

[2] College of Staten Island,Department of Mathematics

[3] City University of New York,undefined

来源：

Journal of Statistical Physics | 2014年 / 157卷

关键词：

Spin glasses; Random energy model; Ground state; Extremal processes; Primary 60G15; 82B44;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the spin glass system consisting of a Random Energy Model coupled with a random magnetic field. This system was investigated by de Oliveira Filho et al. (Phys Rev E 74:031117, 2006) who computed the free energy. In this paper, we recover their result rigorously using elementary large deviations arguments and a conditional second moment method. Our analysis extends at the level of fluctuations of the ground states. In particular, we prove that the joint distribution of the minimal energies has the law of a Poisson process with exponential density after a recentering, which is random as opposed to the standard REM. One consequence is that the Gibbs measure of the model exhibits a one-step replica symmetry breaking as argued by de Oliveira Filho et al. using the replica method.

引用

页码：1 / 16

页数：15

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