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The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree

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Abstract

We study the q-state Potts model on a Cayley tree of order k ≥ 2. In the group representation of the Cayley tree for the ferromagnetic Potts model, we single out a set of index-2 subgroups under which each weakly periodic Gibbs measure is translation invariant. For the anti-ferromagnetic Potts model with k ≥ 2 and q ≥ 2, we show that a weakly periodic Gibbs measure that is not translation invariant is not unique.

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  1. Institute for Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

    M. M. Rahmatullaev

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  1. M. M. Rahmatullaev
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Correspondence to M. M. Rahmatullaev.

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__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 180, No. 3, pp. 307–317, September, 2014.

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Rahmatullaev, M.M. The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree. Theor Math Phys 180, 1019–1029 (2014). https://doi.org/10.1007/s11232-014-0196-4

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  • DOI: https://doi.org/10.1007/s11232-014-0196-4

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