Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree

Sanabel M Abu Oun; Saed Mallak; Jihad Asad

doi:10.1016/j.heliyon.2023.e13418

Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree

Heliyon. 2023 Feb 7;9(2):e13418. doi: 10.1016/j.heliyon.2023.e13418. eCollection 2023 Feb.

Authors

Sanabel M Abu Oun¹, Saed Mallak¹, Jihad Asad²

Affiliations

¹ Department of Applied Mathematics, Faculty of Applied Sciences, Palestine Technical University- Kadoorie, Tulkarm P 305, West Bank, Palestine.
² Department of Physics, Faculty of Applied Sciences, Palestine Technical University- Kadoorie, Tulkarm P 305, West Bank, Palestine.

Abstract

In this paper, we study an Ising-Vannimenus model on a fourth-order semi-infinite Cayley tree with one-level next-nearest-neighbor interactions. We construct the set of translation-invariant Gibbs measures corresponding to the model satisfying Kolmogorov consistency conditions. We prove the existence of the phase transition under specific conditions on the coupling constants and temperature. Numerical examples are presented to clarify the role of the added one-level interactions and results.

Keywords: Cayley tree; Gibbs measures; Ising- Vannimenus model; Phase transition.