Free energies of the Potts model on a Cayley tree

Abstract

Abstract. For the Potts model on the Cayley tree, some explicit formulae of the free energies and entropies (according to vector-valued boundary conditions (BCs)) are obtained. They include translation-invariant, periodic, Dobrushin-like BCs, as well as those corresponding to weakly periodic Gibbs measures.Mathematics Subject Classifications (2010). 82B26 (primary); 60K35 (secondary)

Bubble coalescence in interacting system of DNA molecules

“…Proof. Similar to the proof of Theorem 5.1 in [12], see also the proof of Theorem 1 in [16]. This is 4q − 2 dimensional non-liner system of functional equation.…”

Gibbs measures of Potts model on Cayley trees: a survey and applications

“…References and comments. This review is based on works [10], [27], [28], [29], [34], [31], [32], [36], [39], [40], [45]- [48], [44], [50], [51], [63], [65], [69], [87]- [91], [96], [103]- [105], [107], [110]. Many of these papers written after 2013 and are related to the Potts model on trees.…”