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This article is cited in 4 scientific papers (total in 4 papers)
Nonuniqueness of a Gibbs measure for the Ising ball model
N. M. Khatamov Namangan State University, Namangan, Uzbekistan
Abstract:
We study a new model, the so-called Ising ball model on a Cayley tree of order $k\ge2$. We show that there exists a critical activity $\lambda_{\rm cr}=\sqrt[4]{0.064}$ such that at least one translation-invariant Gibbs measure exists for $\lambda\ge\lambda_{\rm cr}$, at least three translation-invariant Gibbs measures exist for $0<\lambda<\lambda_{\rm cr}$, and for some $\lambda$, there are five translation-invariant Gibbs measures and a continuum of Gibbs measures that are not translation invariant. For any normal divisor $\widehat{G}$ of index $2$ of the group representation on the Cayley tree, we study $\widehat{G}$-periodic Gibbs measures. We prove that there exists an uncountable set of $\widehat{G}$-periodic (not translation invariant and “checkerboard” periodic) Gibbs measures.
Keywords:
Cayley tree, configuration, Ising ball model, Gibbs measure.
Received: 29.03.2014
Citation:
N. M. Khatamov, “Nonuniqueness of a Gibbs measure for the Ising ball model”, TMF, 180:3 (2014), 318–328; Theoret. and Math. Phys., 180:3 (2014), 1030–1039
Linking options:
https://www.mathnet.ru/eng/tmf8685https://doi.org/10.4213/tmf8685 https://www.mathnet.ru/eng/tmf/v180/i3/p318
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Abstract page: | 308 | Full-text PDF : | 151 | References: | 45 | First page: | 9 |
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