Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand

• Date: 2024
• Main Authors: Khakimov, Rustamjon, Umirzakova, Kamola
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024
• Subjects: дерево Кейлi; конфiгурацiя; фертильна модель Hard- core; мiра Гiббса; критична температура; екстремальнiсть мiри
• Online Access: https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1053
• Journal Title: Journal of Mathematical Physics, Analysis, Geometry

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...