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This article is cited in 2 scientific papers (total in 2 papers)
Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree
R. M. Khakimova, F. Kh. Khaidarovb
a Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek, Tashkent, Uzbekistan
b Mirzo Ulugbek National University of Uzbekistan, Tashkent,
Uzbekistan
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 $k\ge3$ that are defined on some invariant sets.
Keywords:
Cayley tree, configuration, Potts model, Gibbs measure, translation-invariant measure, periodic measure
DOI:
https://doi.org/10.4213/tmf9138
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English version:
Theoretical and Mathematical Physics, 2016, 189:2, 1651–1659
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Received: 22.12.2015
Citation:
R. M. Khakimov, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, TMF, 189:2 (2016), 286–295; Theoret. and Math. Phys., 189:2 (2016), 1651–1659
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http://mi.mathnet.ru/eng/tmf9138https://doi.org/10.4213/tmf9138 http://mi.mathnet.ru/eng/tmf/v189/i2/p286
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This publication is cited in the following articles:
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U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 196:1 (2018), 1043–1058
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R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 199:2 (2019), 726–735
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