A certain class of Curie-Weiss models

Details A certain class of Curie-Weiss models A certain class of Curie-Weiss models

2009-06-25

arxiv.org/abs/0906.4673v1

Physics

Mathematical Physics

Scientific paper

By using a formal analogy between statistical mechanics of mean field spin systems and analytical mechanics of viscous liquids -at first pointed out by Francesco Guerra, then recently developed by the authors- we give the thermodynamic limit of the free energy and the critical behavior of Curie Weiss models for a certain class of generalized spin variables. Then, with the same techniques, we give a complete picture of the bipartite Curie-Weiss model, dealing with the same class of generalized spins. Ultimately we analyze further the existence of a minmax principle for the latter which mirrors the standard variational principle of canonical thermodynamics when generalized to multiple interacting parties.

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