Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand
We consider fertile three-state Hard-Core (HC) models with the activityparameter $\lambda >0$ on a Cayley tree. It is known that there exist four types ofsuch models: wrench, wand, hinge, and pipe. These models arise as simpleexamples of loss networks with nearest-neighbor exclusion. In the c...
Збережено в:
| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1053 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | We consider fertile three-state Hard-Core (HC) models with the activityparameter $\lambda >0$ on a Cayley tree. It is known that there exist four types ofsuch models: wrench, wand, hinge, and pipe. These models arise as simpleexamples of loss networks with nearest-neighbor exclusion. In the case wand on a Cayley tree of order $k\ge 2$, exact critical values $\lambda >0$ are found for which two-periodic Gibbs measures are not unique. Moreover, we study the extremality of the existing two-periodic Gibbs measures on a Cayley tree of order two.
Mathematical Subject Classification 2020: 82B26, 60K35 |
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