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Generalized random energy model. II. (English) Zbl 1147.82360
Summary: The formulae for the free energy, when the driving distributions in Generalized Random Energy Model (GREM) are of the form \(Ce^{-|x|^\gamma}\) for \(\gamma \geq 1\) are derived. The large deviation technique allows the use of different distributions at different levels of the GREM. As an illustration we consider, in detail, a two level GREM with exponential and Gaussian distributions. This simple case itself leads to interesting phenomena.
For part I, cf. J. Stat. Phys. 123, No. 5, 1033–1058 (2006; Zbl 1124.82008).
MSC:
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
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