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

Farrukh Mukhamedov, Hasan Akin, Otabek Khakimov

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


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.

Original languageEnglish
Article number053208
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number5
Publication statusPublished - May 17 2017


  • exact results
  • phase diagrams
  • renormalisation group

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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