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On the existence of thermodynamics for the generalized random energy model |
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| Authors: | D. Capocaccia M. Cassandro P. Picco |
| Affiliation: | (1) Centre de Physique Théorique, Centre National de la Recherche Scientifique, Luminy, Marseille, France;(2) Dipartimento di Matematica, Universitá di Roma !["ldquo"]("/content/t002557851882wk0/xlarge8220.gif") La Sapienza!["rdquo"]("/content/t002557851882wk0/xlarge8221.gif") , Rome, Italy;(3) CNR, GNFM, Italy;(4) Dipartimento de Fisica, Universitá di Roma La Sapienza, Rome, Italy;(5) CNR, GNSM, Université de Provence, Italy |
| Abstract: | Derrida's generalized random energy model is considered. Almost sure andLp convergence of the free energy at any inverse temperature 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. |
| Keywords: | Random energy random variables spin glass |
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