Research PapersNo Access

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

Hasan Akın

Department of Mathematics, Faculty of Education, Zirve University, 27260 Gaziantep, Turkey

https://doi.org/10.1142/S021797921750093XCited by:14 (Source: Crossref)

Abstract

Ising model with competing nearest–neighbors (NN) and prolonged next–nearest–neighbors (NNN) 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 NN and prolonged NNN interactions on a Cayley tree (or Bethe lattice) of order three. By using a new approach, we describe the translation-invariant Gibbs measures (TIGMs) for the model. We show that some of the measures are extreme Gibbs distributions. In this paper, we try to determine when phase transition does occur.

Keywords:

PACS: 05.70.Fh, 05.70.Ce, 75.10.Hk

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