Cayley树上Blume-Capel hc模型Gibbs测度的极值性

Pub Date : 2022-06-01 DOI:10.35634/vm220207

Khatamov N.M.

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引用次数: 0

摘要

本文考虑了二阶Cayley树上“广义棒”的blme - capel模型的平移不变Gibbs测度(TIGM)。发现$\theta_{cr}$的近似临界值使得$\theta \geq\theta_{cr}$只有一个TIGM，而对于$0<\theta<\theta_{cr}$，在考虑模型的“广义棒”情况下，正好有三个TIGM。此外，还研究了这些测度的(非)极值问题。

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Extremality of some Gibbs measures for the Blume–Capel HC-model on a Cayley tree

In this paper, we consider translation-invariant Gibbs measures (TIGM) for the Blume–Capel HC-model in the case of a “generalized wand” on a second-order Cayley tree. An approximate critical value of $\theta_{cr}$ is found such that for $\theta \geq\theta_{cr}$ there is only one TIGM, and for $0<\theta<\theta_{cr}$ there are exactly three TIGMs in the case of “generalized wand” for the model under consideration. In addition, the (non)extreme problem for these measures is studied.

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