D. Gandolfo, M. M. Rakhmatullaev, U. A. Rozikov, J. Ruiz
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 include 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.
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http://arxiv.org/abs/1211.6648
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