On Ground States and Phase Transition for $\lambda$-Model with the Competing Potts Interactions on Cayley Trees
Abstract
In this paper, we consider the -model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if -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.
Cite
@article{arxiv.1904.06190,
title = {On Ground States and Phase Transition for $\lambda$-Model with the Competing Potts Interactions on Cayley Trees},
author = {Farrukh Mukhamedov and Chin Hee Pah and Hakim Jamil and Muzaffar Rahmatullaev},
journal= {arXiv preprint arXiv:1904.06190},
year = {2020}
}
Comments
23 pages. arXiv admin note: text overlap with arXiv:1704.01933