On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
In this paper, we continue an investigation of the p-adic Ising– Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional p-adic system of equations. We are also able to show the uni...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute of Physics Publishing Ltd.
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/44018/ http://irep.iium.edu.my/44018/1/mfmsokh-jstat-2015.pdf |
| _version_ | 1848782539153473536 |
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| author | Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek |
| author_facet | Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | In this paper, we continue an investigation of the p-adic Ising–
Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove
the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional
p-adic system of equations. We are also able to show the uniqueness
of translation-invariant p-adic Gibbs measure. Finally, it is established the
existence of the phase transition for the Ising–Vannimenus model depending on
the order k of the Cayley tree and the prime p. Note that the methods used in
the paper are not valid in the real setting, since all of them are based on p-adic
analysis and p-adic probability measures. |
| first_indexed | 2025-11-14T16:07:04Z |
| format | Article |
| id | iium-44018 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:07:04Z |
| publishDate | 2015 |
| publisher | Institute of Physics Publishing Ltd. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-440182019-04-09T02:03:41Z http://irep.iium.edu.my/44018/ On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek QA Mathematics QC Physics In this paper, we continue an investigation of the p-adic Ising– Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional p-adic system of equations. We are also able to show the uniqueness of translation-invariant p-adic Gibbs measure. Finally, it is established the existence of the phase transition for the Ising–Vannimenus model depending on the order k of the Cayley tree and the prime p. Note that the methods used in the paper are not valid in the real setting, since all of them are based on p-adic analysis and p-adic probability measures. Institute of Physics Publishing Ltd. 2015-05 Article PeerReviewed application/pdf en http://irep.iium.edu.my/44018/1/mfmsokh-jstat-2015.pdf Mukhamedov, Farrukh and Saburov, Mansoor and Khakimov, Otabek (2015) On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree. Journal of Statistical Mechanics: Theory and Experiment, 2015 (5). P05032. ISSN 1742-5468 (O) http://dx.doi.org/10.1088/1742-5468/2015/05/P05032 10.1088/1742-5468/2015/05/P05032 |
| spellingShingle | QA Mathematics QC Physics Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree |
| title | On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree |
| title_full | On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree |
| title_fullStr | On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree |
| title_full_unstemmed | On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree |
| title_short | On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree |
| title_sort | on p-adic ising–vannimenus model on an arbitrary order cayley tree |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/44018/ http://irep.iium.edu.my/44018/ http://irep.iium.edu.my/44018/ http://irep.iium.edu.my/44018/1/mfmsokh-jstat-2015.pdf |