Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree |
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Authors: | R. M. Khakimov F. Kh. Khaydarov |
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Affiliation: | 1.Institute of Mathematics,Mirzo Ulugbek National University of Uzbekistan,Tashkent,Uzbekistan;2.Mirzo Ulugbek National University of Uzbekistan,Tashkent,Uzbekistan |
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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. |
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