Article

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

Theoretical and Mathematical Physicsjournal2016en

ABI

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.

Topics

Theoretical and Computational Physics Random Matrices and Applications Stochastic processes and statistical mechanics

Identifiers

DOI: 10.1134/s004057791611009x

Citations and references

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