Phase transition and Gibbs Measures of Vannimenus model on semi-infinite Cayley tree of order three

Abstract

Ising model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree has long been studied but there are still many problems untouched. This paper tackles new Gibbs measures of Ising-Vannimenus model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree (or Bethe lattice) of order three. By using a new approach, we describe the translation-invariant Gibbs measures for the model. We show that some of the measures are extreme Gibbs distributions. In this paper we take up with trying to determine when phase transition does occur.

16 pages, 5 figures. Some minor mistakes are corrected. The paper are improved

References in corpus (1)

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

Cited by in corpus (3)

• Gibbs measures and free energies of Ising-Vannimenus Model on the Cayley tree
• Gibbs Measures with memory of length 2 on an arbitrary order Cayley tree
• Determination of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree