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- Title
Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree.
- Authors
Hatamov, N.; Madgoziev, G.
- Abstract
We study a generalized Potts model on a Cayley tree of order k = 3. Under some conditions on the parameters, we show that there exist at most two translation-invariant Gibbs measures and a continuum of Gibbs measures that are not translation invariant. For any index-two normal divisor Ĝ of the group realizing the Cayley tree, we study Ĝ-periodic Gibbs measures. The existence of an uncountable set of Ĝ-periodic Gibbs measures (which are not translation invariant and not 'checkerboard' periodic) is proved.
- Subjects
POTTS model; GIBBS' free energy; PHASE transitions; CAYLEY graphs; INVARIANTS (Mathematics)
- Publication
Theoretical & Mathematical Physics, 2015, Vol 183, Issue 3, p836
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1007/s11232-015-0300-4