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- Title
On Weakly Periodic Gibbs Measures for the Potts Model with External Field on the Cayley Tree.
- Authors
Rakhmatullaev, M.
- Abstract
We study the Potts model with external field on a Cayley tree of order k ≥ 2. For the antiferromagnetic Potts model with external field and k ≥ 6 and q ≥ 3, it is shown that the weakly periodic Gibbs measure, which is not periodic, is not unique. For the Potts model with external field equal to zero, we also study weakly periodic Gibbs measures. It is shown that, under certain conditions, the number of these measures cannot be smaller than 2 − 2.
- Subjects
ANTIFERROMAGNETIC materials; POTTS model; CAYLEY graphs; PERIODIC functions; MATHEMATICAL analysis
- Publication
Ukrainian Mathematical Journal, 2016, Vol 68, Issue 4, p598
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-016-1244-z