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

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 existenc...

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Detalles Bibliográficos
Autores principales: Abu Oun, Sanabel M., Mallak, Saed, Asad, Jihad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2023
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9958442/
https://www.ncbi.nlm.nih.gov/pubmed/36852055
http://dx.doi.org/10.1016/j.heliyon.2023.e13418
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author Abu Oun, Sanabel M.
Mallak, Saed
Asad, Jihad
author_facet Abu Oun, Sanabel M.
Mallak, Saed
Asad, Jihad
author_sort Abu Oun, Sanabel M.
collection PubMed
description 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.
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spelling pubmed-99584422023-02-26 Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree Abu Oun, Sanabel M. Mallak, Saed Asad, Jihad Heliyon Research Article 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. Elsevier 2023-02-07 /pmc/articles/PMC9958442/ /pubmed/36852055 http://dx.doi.org/10.1016/j.heliyon.2023.e13418 Text en © 2023 The Authors https://creativecommons.org/licenses/by/4.0/This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Research Article
Abu Oun, Sanabel M.
Mallak, Saed
Asad, Jihad
Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree
title Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree
title_full Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree
title_fullStr Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree
title_full_unstemmed Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree
title_short Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree
title_sort gibbs measures of an ising-vannimenus model with one-level competing interactions on 4th order cayley tree
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9958442/
https://www.ncbi.nlm.nih.gov/pubmed/36852055
http://dx.doi.org/10.1016/j.heliyon.2023.e13418
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