The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree |
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Authors: | M. M. Rahmatullaev |
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Affiliation: | 1. Institute for Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
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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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