Abstract
Derrida's generalized random energy model is considered. Almost sure andL p convergence of the free energy at any inverse temperatureβ are proven for an arbitrary numbern of hierarchical levels. The explicit form of the free energy is given in the most general case and the limitn→∞ is discussed.
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Capocaccia, D., Cassandro, M. & Picco, P. On the existence of thermodynamics for the generalized random energy model. J Stat Phys 46, 493–505 (1987). https://doi.org/10.1007/BF01013370
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DOI: https://doi.org/10.1007/BF01013370