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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| Format: | Article |
| Language: | English English English |
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Maik Nauka Publishing / Springer SBM
2016
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| Online Access: | 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 |
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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 | 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. |
| first_indexed | 2025-11-14T16:47:42Z |
| format | Article |
| id | iium-58349 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T16:47:42Z |
| publishDate | 2016 |
| publisher | Maik Nauka Publishing / Springer SBM |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| 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 |
| title | 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_short | 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 |
| topic | Q Science (General) |
| 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 |