Ground States and Phase Transition of the λ Model on the Cayley Tree

F. Mukhamedov; Chin Hee Pah; H. Jamil

doi:10.1134/S004057791802006X

Ground States and Phase Transition of the λ Model on the Cayley Tree

Authors: Mukhamedov F.¹, Pah C.H.², Jamil H.²
Affiliations:
1. Department of Mathematical Sciences, College of Science
2. Department of Computational and Theoretical Sciences, Faculty of Science
Issue: Vol 194, No 2 (2018)
Pages: 260-273
Section: Article
URL: https://journals.rcsi.science/0040-5779/article/view/171635
DOI: https://doi.org/10.1134/S004057791802006X
ID: 171635

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Abstract

We consider the λ model, a generalization of the Potts model, with spin values {1, 2, 3} on the order-two Cayley tree. We describe the model ground states and prove that translation-invariant Gibb measures exist, which means that a phase transition exists. We establish that two-periodic Gibbs measures exist.