Article ID Journal Published Year Pages File Type
1783786 Chinese Journal of Physics 2016 15 Pages PDF
Abstract
In this paper, we consider Vannimenus model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree. For this model we define Markov random fields with memory of length 2. By using a new approach, we obtain new sets of Gibbs measures of Ising-Vannimenus model on Cayley tree of order 2. We construct the recurrence equations corresponding Ising-Vannimenus model. We prove the Kolmogorov consistency condition. We investigate the translation-invariant and periodic non transition-invariant Gibbs measures for the model. We find new sets of Gibbs measures different from the Gibbs measures given in the references Mukhamedov and Akın (2015) and Ganikhodjaev et al. (2011). We show that some of the measures are extreme Gibbs distributions.
Related Topics
Physical Sciences and Engineering Physics and Astronomy Atomic and Molecular Physics, and Optics
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