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