Abstract
We study the extreme value statistics of the two-level Generalized Random Energy Model (GREM) coupled with a random magnetic field. This model generalizes both the Random Energy Model (REM) combined with a random magnetic field studied by de Oliveira Filho et al. and Arguin and Kistler, and that of the GREM in the presence of a uniform external field studied by Bovier and Klimovsky. The extreme value statistics of the model are determined at the level of the entropy and of the free energy, generalizing the behavior found in Arguin and Kistler and Bovier and Klimovsky. The proofs rely on an application of large deviation theory which reduces the problem to that of a GREM on a subset of configurations for which the magnetization attains a specific value. The methods introduced are general and extend to the k-level GREM in the presence of a random magnetic field.
The research of L.-P. A. is supported in part by NSF CAREER DMS-1653602.
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Arguin, LP., Persechino, R. (2019). The Free Energy of the GREM with Random Magnetic Field. In: Gayrard, V., Arguin, LP., Kistler, N., Kourkova, I. (eds) Statistical Mechanics of Classical and Disordered Systems . StaMeClaDys 2018. Springer Proceedings in Mathematics & Statistics, vol 293. Springer, Cham. https://doi.org/10.1007/978-3-030-29077-1_3
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