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arXiv · 1510.08405

Using New Approaches to obtain Gibbs Measures of Vannimenus model on a Cayley tree

Hasan Akin
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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 \cite{NHSS,FreeMA}. We show that some of the measures are extreme Gibbs distributions.

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Hasan Akin. 2016-10-09. Using New Approaches to obtain Gibbs Measures of Vannimenus model on a Cayley tree. https://doi.org/10.1016/j.cjph.2016.07.010

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