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TMF, 2019, Volume 199, Number 2, Pages 291–301 (Mi tmf9574)  

Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree

R. M. Khakimov, M. T. Makhammadaliev

Namangam State University, Namangan, Uzbekistan

Abstract: We study the Potts model with a zero external field on the Cayley tree. For the antiferromagnetic Potts model with $q$ states on a second-order Cayley tree and for the ferromagnetic Potts model with $q$ states on a $k$th-order Cayley tree, we show that all periodic Gibbs measures are translation-invariant for all parameter values.

Keywords: Cayley tree, configuration, Potts model, Gibbs measure, periodic measure, translation-invariant measure.

DOI: https://doi.org/10.4213/tmf9574

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English version:
Theoretical and Mathematical Physics, 2019, 199:2, 726–735

Bibliographic databases:

Received: 11.03.2018
Revised: 24.10.2018

Citation: R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, TMF, 199:2 (2019), 291–301; Theoret. and Math. Phys., 199:2 (2019), 726–735

Citation in format AMSBIB
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\pages 291--301
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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