2019/04/11 by Farrukh Mukhamedov, Chin Hee Pah, Hakim Jamil +1
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1016/j.physa.2020.124184
23 pages. arXiv admin note: text overlap with arXiv:1704.01933
arxiv created 2019/04/11 · arxiv updated 2020/05/20
In this paper, we consider the λ-model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if λ-function is taken as a Potts interaction function, then this model contains as a particular case of Potts model with competing interactions on Cayley tree. In this paper, we first describe all ground states of the model. We point out that the Potts model with considered interactions was investigated only numerically, without rigorous (mathematical) proofs. One of the main points of this paper is to propose a measure-theoretical approach for the considered model in more general setting. Furthermore, we find certain conditions for the existence of Gibbs measures corresponding to the model, which allowed to establish the existence of the phase transition.