Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree
- Authors: Khakimov R.M.1, Khaydarov F.K.2
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Affiliations:
- Institute of Mathematics
- Mirzo Ulugbek National University of Uzbekistan
- Issue: Vol 189, No 2 (2016)
- Pages: 1651-1659
- Section: Article
- URL: https://journals.rcsi.science/0040-5779/article/view/170847
- DOI: https://doi.org/10.1134/S004057791611009X
- ID: 170847
Cite item
Abstract
We study translation-invariant Gibbs measures on a Cayley tree of order k = 3 for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order k for the antiferromagnetic q-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order k ≥ 3 that are defined on some invariant sets.
About the authors
R. M. Khakimov
Institute of Mathematics
Author for correspondence.
Email: rustam-7102@rambler.ru
Uzbekistan, Tashkent
F. Kh. Khaydarov
Mirzo Ulugbek National University of Uzbekistan
Email: rustam-7102@rambler.ru
Uzbekistan, Tashkent