ON FREE ENERGIES OF THE ISING MODEL ON THE CAYLEY TREE
Daniel GandolfoCPT - Centre de Physique Théorique - UMR 6207 (Aix-Marseille Université Case 907 13288 Marseille cedex 9 Université de Toulon 83957 La Garde - France)M. M. RakhmatullaevNamangan State University (Uzbekistan)U. A. RozikovJ. RuizCPT - Centre de Physique Théorique - UMR 6207 (Aix-Marseille Université Case 907 13288 Marseille cedex 9 Université de Toulon 83957 La Garde - France)
2016en
ABI
Abstract
Abstract. We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They in-clude translation-invariant, periodic, Dobrushin-like b.c., as well as those corresponding to (recently discovered) weakly periodic Gibbs states. The later are defined through a partition of the tree that induces a 4-edge-coloring. We compute the density of each color. Mathematics Subject Classifications (2010). 82B26 (primary); 60K35 (sec-ondary)
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