On Ground States and Phase Transition for $\lambda$-Model with the Competing Potts Interactions on Cayley Trees

Abstract

In this paper, we consider the $\lambda$-model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if $\lambda$-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.

arXiv comment23 pages. arXiv admin note: text overlap with arXiv:1704.01933

References in corpus (4)

• Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists
• Potts model on complex networks
• Phase diagram of the three states Potts model with next nearest neighbor interactions on the Bethe lattice
• Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart