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

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.

18 Pages, 11 figures, Chinese Journal of Physics 2016

References in corpus (1)

• On $P$-adic Ising-Vannimenus model on an arbitrary order Cayley tree

Cited by in corpus (7)

• Gibbs measures and free energies of Ising-Vannimenus Model on the Cayley tree
• Phase transition and Gibbs Measures of Vannimenus model on semi-infinite Cayley tree of order three
• Gibbs Measures with memory of length 2 on an arbitrary order Cayley tree
• Gibbs measures of an Ising model with competing interactions on the triangular chandelier-lattice
• Determination of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree
• Phase diagrams of lattice models on Cayley tree and chandelier network: a review
• Exact description of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree