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...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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oai:jmag.ilt.kharkiv.ua:article-10532024-12-10T20:10:54Z Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand Khakimov, Rustamjon Umirzakova, Kamola дерево Кейлi конфiгурацiя фертильна модель Hard- core мiра Гiббса критична температура екстремальнiсть мiри Cayley tree configuration fertile Hard-core model Gibbs measure critical temperature extreme measure 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 Ми розглядаємо фертильнi (Hard-Core) HC-моделi з трьома стана-ми з параметром активностi $\lambda >0$ на деревi Кейлi. Вiдомо, що iснуютьчотири типи таких моделей: гайковий ключ, паличка, петля i труба. Цiмоделi виникають як простi приклади втрат взаємодiї з найближчимсусiдом. У випадку “палички” на деревi Кейлi порядку $k\ge 2$ знайденоточнi критичнi значення $\lambda >0$, для яких двоперiодичнi мiри Гiббса неє єдиними. Крiм того, ми вивчаємо екстремальнiсть iснуючих двоперiо-дичних мiр Гiббса на деревi Кейлi другого порядку. Mathematical Subject Classification 2020: 82B26, 60K35 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024-04-01 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1053 10.15407/mag20.01.066 Journal of Mathematical Physics, Analysis, Geometry; Vol. 20 No. 1 (2024); 66–81 Журнал математической физики, анализа, геометрии; Том 20 № 1 (2024); 66–81 Журнал математичної фізики, аналізу, геометрії; Том 20 № 1 (2024); 66–81 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1053/jm20-0066e |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
| baseUrl_str |
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| datestamp_date |
2024-12-10T20:10:54Z |
| collection |
OJS |
| language |
English |
| topic |
дерево Кейлi конфiгурацiя фертильна модель Hard- core мiра Гiббса критична температура екстремальнiсть мiри |
| spellingShingle |
дерево Кейлi конфiгурацiя фертильна модель Hard- core мiра Гiббса критична температура екстремальнiсть мiри Khakimov, Rustamjon Umirzakova, Kamola Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand |
| topic_facet |
дерево Кейлi конфiгурацiя фертильна модель Hard- core мiра Гiббса критична температура екстремальнiсть мiри Cayley tree configuration fertile Hard-core model Gibbs measure critical temperature extreme measure |
| format |
Article |
| author |
Khakimov, Rustamjon Umirzakova, Kamola |
| author_facet |
Khakimov, Rustamjon Umirzakova, Kamola |
| author_sort |
Khakimov, Rustamjon |
| title |
Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand |
| title_short |
Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand |
| title_full |
Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand |
| title_fullStr |
Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand |
| title_full_unstemmed |
Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand |
| title_sort |
periodic gibbs measures for three-state hard-core models in the case wand |
| title_alt |
Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand |
| description |
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 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2024 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1053 |
| work_keys_str_mv |
AT khakimovrustamjon periodicgibbsmeasuresforthreestatehardcoremodelsinthecasewand AT umirzakovakamola periodicgibbsmeasuresforthreestatehardcoremodelsinthecasewand |
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2025-09-26T01:40:42Z |
| last_indexed |
2025-09-26T01:40:42Z |
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1850836863449825280 |