Farrukh Mukhamedov, Hasan Akin
Published 2015-04-03Version 1
In this paper, we consider Ising-Vannimenus model on a Cayley tree for order two with competing nearest-neighbor, prolonged next-nearest neighbor interactions. We stress that the mentioned model was investigated only numerically, without rigorous (mathematical) proofs. One of the main point of this paper is to propose a measure-theoretical approach the considered model. We find certain conditions for the existence of Gibbs measures corresponding to the model. Then we establish the existence of the phase transition. Moreover, the free energies of the found Gibbs measures are calculated.
On free energies of the Ising model on the Cayley tree
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On free energies of the Potts model on the Cayley tree
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