Translation-invariant extreme Gibbs measures for the Blume–Capel model with a wand on a Cayley tree

Keywords: configuration, Cayley tree, Gibbs measures

Abstract

UDC 517.98

We study the translation-invariant Gibbs measures for the Blume–Capel model with a wand on a Cayley tree of order $k.$  We find the exact critical value $\theta_{cr}=1$ such that there exists a unique translation-invariant Gibbs measure for $\theta \geq\theta_{cr}$ and there exist exactly three translation-invariant Gibbs measures for $0<\theta<\theta_{cr}$ in the case of a wand for the model.  In addition, we investigate the problem of (non)extremes for these measures.

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Published
28.03.2020
How to Cite
Khatamov N. M. “Translation-Invariant Extreme Gibbs Measures for the Blume–Capel Model With a Wand on a Cayley Tree”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 4, Mar. 2020, pp. 540-56, doi:10.37863/umzh.v72i4.2281.
Section
Research articles