Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree

We consider the p-adic Ising–Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory (in the p-adic sense) and describe all translation-invariant p-adic quas...

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Main Authors:	Mukhamedov, Farrukh, Saburov, Mansoor, Khakimov, Otabek
Format:	Article
Language:	English English English
Published:	Maik Nauka Publishing / Springer SBM 2016
Subjects:	Q Science (General)
Online Access:	http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/1/58349_Translation-invariant%20p-adic%20quasi.pdf http://irep.iium.edu.my/58349/2/58349_Translation-invariant%20p-adic%20quasi_SCOPUS.pdf http://irep.iium.edu.my/58349/3/58349_Translation-invariant%20p-adic%20quasi_WOS.pdf

id	iium-58349
recordtype	eprints
spelling	iium-583492017-10-05T08:49:26Z http://irep.iium.edu.my/58349/ Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek Q Science (General) We consider the p-adic Ising–Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory (in the p-adic sense) and describe all translation-invariant p-adic quasi-Gibbs measures associated with the model. As a consequence, we can prove that a phase transition exists in the model. Here, “phase transition” means that there exist at least two nontrivial p-adic quasi-Gibbs measures such that one is bounded and the other is unbounded. The methods used are inapplicable in the real case. © 2016, Pleiades Publishing, Ltd. Maik Nauka Publishing / Springer SBM 2016-04-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/58349/1/58349_Translation-invariant%20p-adic%20quasi.pdf application/pdf en http://irep.iium.edu.my/58349/2/58349_Translation-invariant%20p-adic%20quasi_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/58349/3/58349_Translation-invariant%20p-adic%20quasi_WOS.pdf Mukhamedov, Farrukh and Saburov, Mansoor and Khakimov, Otabek (2016) Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree. Theoretical and Mathematical Physics(Russian Federation), 187 (1). pp. 583-602. ISSN 0040-5779 E-ISSN 1573-9333 https://link.springer.com/article/10.1134/S0040577916040127 10.1134/S0040577916040127
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	Q Science (General)
spellingShingle	Q Science (General) Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
description	We consider the p-adic Ising–Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory (in the p-adic sense) and describe all translation-invariant p-adic quasi-Gibbs measures associated with the model. As a consequence, we can prove that a phase transition exists in the model. Here, “phase transition” means that there exist at least two nontrivial p-adic quasi-Gibbs measures such that one is bounded and the other is unbounded. The methods used are inapplicable in the real case. © 2016, Pleiades Publishing, Ltd.
format	Article
author	Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek
author_facet	Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek
author_sort	Mukhamedov, Farrukh
title	Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
title_short	Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
title_full	Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
title_fullStr	Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
title_full_unstemmed	Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
title_sort	translation-invariant p-adic quasi-gibbs measures for the ising–vannimenus model on a cayley tree
publisher	Maik Nauka Publishing / Springer SBM
publishDate	2016
url	http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/1/58349_Translation-invariant%20p-adic%20quasi.pdf http://irep.iium.edu.my/58349/2/58349_Translation-invariant%20p-adic%20quasi_SCOPUS.pdf http://irep.iium.edu.my/58349/3/58349_Translation-invariant%20p-adic%20quasi_WOS.pdf
first_indexed	2023-09-18T21:22:30Z
last_indexed	2023-09-18T21:22:30Z
_version_	1777411975283736576

Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree

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