Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree
R. M. KhakimovInstitute of Mathematics, Mirzo Ulugbek National University of Uzbekistan, Tashkent, UzbekistanF. Kh. KhaydarovMirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan
ABI
Annotatsiya
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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