Gibbs measures and free energies of Ising–Vannimenus model on the Cayley tree. (17th May 2017)

• Record Type: Journal Article
• Authors: Mukhamedov, Farrukh; Akın, Hasan; Khakimov, Otabek
• Is Part Of: Journal of statistical mechanics. (2017:May)
• Publication Date: 2017-05-17
• Subjects: 11 -- 3; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa6c88
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: In this paper, we consider the Ising–Vannimenus model on a Cayley tree for order two with competing nearest-neighbor and prolonged next-nearest neighbor interactions. We stress that the mentioned model 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. We find certain conditions for the existence of Gibbs measures corresponding to the model, which allowed to establish the existence of the phase transition. Moreover, the free energies and entropies, associated with translation invariant Gibbs measures, are calculated.