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Семинар лаборатории теории функций "Современные проблемы комплексного анализа"
9 ноября 2023 г. 11:30–12:30, г. Ташкент, Онлайн на платформе Zoom
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Gibbs measures for the HC-Blum—Kapel model with a countable number of states on the Cayley tree
N. M. Khatamov V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan, Tashkent
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Эта страница: | 80 |
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Аннотация:
The report is devoted to the study of the Gibbs measure for the HC-Blum—Kapel model with a countable set of $\mathbb{Z}$ spin values and the interaction strength $J\in \mathbb{R}$ of nearest neighbors on the Cayley tree of order $k\ge 2 $. Conditions for the existence and non-existence of a translation-invariant Gibbs measure are found and the uniqueness of such a measure is proved under the condition of existence. In addition, for the model under consideration, periodic Gibbs measures with period two are studied and the exact value of the parameter ${{\Theta }_{cr}}$ is found such that for $0<\Theta \le {{\Theta }_{cr}} $ there is exactly one periodic Gibbs measure ${{\mu }_{0}}$, which is translation-invariant, and for $\Theta >{{\Theta }_{cr}}$ there are exactly three periodic Gibbs measures $ {{\mu }_{0}},\,\,{{\mu }_{1}},\,\,{{\mu }_{2}}$, where the measures ${{\mu } _{1}},\,\,{{\mu }_{2}}$ are periodic (non-translation invariant) Gibbs measures with period two.
Website:
https://us02web.zoom.us/j/8022228888?pwd=b3M4cFJxUHFnZnpuU3kyWW8vNzg0QT09
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