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TMF, 2015, Volume 183, Number 3, Pages 450–459 (Mi tmf8702)  

Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree

N. M. Khatamov, G. T. Madgoziev

Namangan State University, Namangan, Uzbekistan

Abstract: We study a generalized Potts model on a Cayley tree of order $k=3$. Under some conditions on the parameters, we show that there exist at most two translation-invariant Gibbs measures and a continuum of Gibbs measures that are not translation invariant. For any index-two normal divisor $\widehat G$ of the group realizing the Cayley tree, we study $\widehat hG$-periodic Gibbs measures. The existence of an uncountable set of $\widehat hG$-periodic Gibbs measures (which are not translation invariant and not “checkerboard” periodic) is proved.

Keywords: Cayley tree, configuration, generalized Potts model, Gibbs measure

DOI: https://doi.org/10.4213/tmf8702

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English version:
Theoretical and Mathematical Physics, 2015, 183:3, 836–845

Bibliographic databases:

Received: 01.05.2014
Revised: 17.09.2014

Citation: N. M. Khatamov, G. T. Madgoziev, “Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree”, TMF, 183:3 (2015), 450–459; Theoret. and Math. Phys., 183:3 (2015), 836–845

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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