Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand
DOI:
https://doi.org/10.15407/mag20.01.066Анотація
Ми розглядаємо фертильнi (Hard-Core) HC-моделi з трьома стана-
ми з параметром активностi $\lambda >0$ на деревi Кейлi. Вiдомо, що iснують
чотири типи таких моделей: гайковий ключ, паличка, петля i труба. Цi
моделi виникають як простi приклади втрат взаємодiї з найближчим
сусiдом. У випадку “палички” на деревi Кейлi порядку $k\ge 2$ знайдено
точнi критичнi значення $\lambda >0$, для яких двоперiодичнi мiри Гiббса не
є єдиними. Крiм того, ми вивчаємо екстремальнiсть iснуючих двоперiо-
дичних мiр Гiббса на деревi Кейлi другого порядку.
Mathematical Subject Classification 2020: 82B26, 60K35
Ключові слова:
дерево Кейлi, конфiгурацiя, фертильна модель Hard- core, мiра Гiббса, критична температура, екстремальнiсть мiриПосилання
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