Gibbs measures and free energies of Ising-Vannimenus Model on the Cayley tree

2017/04/06 by Farrukh Mukhamedov, Hasan Akin, Otabek Khakimov · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP

paper · pdf · doi:10.1088/1742-5468/aa6c88

published as Journal of Stat Mech. Theory & Exp. 2017, 053208 · 15 pages, 2 figures. arXiv admin note: text overlap with arXiv:1504.00755

arxiv created 2017/04/06 · arxiv updated 2017/08/15

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.

Citations

• Gibbs measures and free energies of the Ising-Vannimenus Model on the Cayley tree

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