随机磁场中随机能量模型的微正则分析
Microcanonical analysis of the Random Energy Model in a random magnetic field
摘要：
本文研究了由随机能量模型和随机磁场组成的自旋玻璃系统。de Oliveira Filho、da Costa和Yokoi（Phys. Rev. E 74 [2006]）研究了该系统，并计算了自由能。本文利用初等大偏差变元和条件二阶矩方法，严格地恢复了他们的结果。我们的分析扩展到基态的波动水平。特别是，我们证明了联合分布的极值能量具有规律的泊松过程的指数密度后，重中心，这是随机的，而不是标准的REM。一个结果是，该模型的吉布斯测度表现出一个单步副本对称性破缺，正如de Oliveira Filho等人使用副本方法所论证的那样。
英文摘要：
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, da Costa and Yokoi (Phys. Rev. E 74 [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 extremal 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.
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