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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).
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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