Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree. Issue 2 (February 2023)

• Record Type: Journal Article
• Authors: Abu Oun, Sanabel M.; Mallak, Saed; Asad, Jihad
• Is Part Of: Heliyon. Volume 9:Issue 2(2023)
• Publication Date: 2023-02
• Subjects: Cayley tree -- Gibbs measures -- Ising- Vannimenus model -- Phase transition; Research -- Periodicals; Medical sciences -- Periodicals; Natural history -- Periodicals; Social sciences -- Periodicals; Earth sciences -- Periodicals; Physical sciences -- Periodicals; 507.2
• DOI: 10.1016/j.heliyon.2023.e13418
• Languages: English
• ISSNs: 2405-8440

Abstract

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.