A certain class of Curie-Weiss models
Mathematical Physics
2009-06-26 v1 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.0906.4673,
title = {A certain class of Curie-Weiss models},
author = {Giuseppe Genovese and Adriano Barra},
journal= {arXiv preprint arXiv:0906.4673},
year = {2009}
}