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This article is cited in 16 scientific papers (total in 16 papers)
The existence of weakly periodic Gibbs measures for the Potts model on
a Cayley tree
M. M. Rakhmatullaev Institute for Mathematics, National University of Uzbekistan,
Tashkent, Uzbekistan
Abstract:
We study the $q$-state Potts model on a Cayley tree of order $k\ge2$. 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 $k\ge2$ and $q\ge 2$, we show that a weakly periodic Gibbs measure that is not translation invariant is not unique.
Keywords:
Cayley tree, Gibbs measure, Potts model, weakly periodic Gibbs measure.
Received: 01.02.2014
Citation:
M. M. Rakhmatullaev, “The existence of weakly periodic Gibbs measures for the Potts model on
a Cayley tree”, TMF, 180:3 (2014), 307–317; Theoret. and Math. Phys., 180:3 (2014), 1019–1029
Linking options:
https://www.mathnet.ru/eng/tmf8647https://doi.org/10.4213/tmf8647 https://www.mathnet.ru/eng/tmf/v180/i3/p307
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Abstract page: | 313 | Full-text PDF : | 152 | References: | 51 | First page: | 13 |
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