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

作者：Arguin Louis Pierre^*; Kistler Nicola

来源：Journal of Statistical Physics, 2014, 157(1): 1-16.

DOI：10.1007/s10955-014-1072-1

• Spin glasses
• Random energy model
• Ground state
• Extremal processes

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.

• 出版日期2014-10