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

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.

15 pages, 2 figures. arXiv admin note: text overlap with arXiv:1504.00755

References in corpus (3)

• Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart
• Using New Approaches to obtain Gibbs Measures of Vannimenus model on a Cayley tree
• Phase transition and Gibbs Measures of Vannimenus model on semi-infinite Cayley tree of order three

Cited by in corpus (2)

• Gibbs Measures with memory of length 2 on an arbitrary order Cayley tree
• Determination of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree