Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree
In this present paper, we consider the p-adic Ising Vannimenus model on the Cayley tree of order two. A new measure-theoretical approach (in the p-adic sense) to investigate such a model is proposed. The main result of this paper is to establish the existence of the phase transition for the model. B...
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| Format: | Article |
| Language: | English English |
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IOP Publishing Ltd.
2014
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| Online Access: | http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/1/mfmdha-JSTAT%282014%29.pdf http://irep.iium.edu.my/38902/4/38902_Phase%20transition_scopus_new.pdf |
| _version_ | 1848781690438156288 |
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| author | Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan |
| author_facet | Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | In this present paper, we consider the p-adic Ising Vannimenus model on the Cayley tree of order two. A new measure-theoretical approach (in the p-adic sense) to investigate such a model is proposed. The main result of this paper is to establish the existence of the phase transition for the model. By the phase transition we mean the existence of at least two non-trivial p-adic quasi Gibbs measures, such that one is bounded and the second one is unbounded (note that in the p-adic probability, unlike a real setting, the probability measures could even be unbounded). To prove the main result, we investigate a nonlinear recurrence equation via the methods of p-adic analysis. Note that the methods used in the paper are not valid in a real setting |
| first_indexed | 2025-11-14T15:53:34Z |
| format | Article |
| id | iium-38902 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T15:53:34Z |
| publishDate | 2014 |
| publisher | IOP Publishing Ltd. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-389022017-09-25T07:47:50Z http://irep.iium.edu.my/38902/ Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan QA Mathematics QC Physics In this present paper, we consider the p-adic Ising Vannimenus model on the Cayley tree of order two. A new measure-theoretical approach (in the p-adic sense) to investigate such a model is proposed. The main result of this paper is to establish the existence of the phase transition for the model. By the phase transition we mean the existence of at least two non-trivial p-adic quasi Gibbs measures, such that one is bounded and the second one is unbounded (note that in the p-adic probability, unlike a real setting, the probability measures could even be unbounded). To prove the main result, we investigate a nonlinear recurrence equation via the methods of p-adic analysis. Note that the methods used in the paper are not valid in a real setting IOP Publishing Ltd. 2014-10 Article PeerReviewed application/pdf en http://irep.iium.edu.my/38902/1/mfmdha-JSTAT%282014%29.pdf application/pdf en http://irep.iium.edu.my/38902/4/38902_Phase%20transition_scopus_new.pdf Mukhamedov, Farrukh and Dogan, Mutlay and Akin, Hasan (2014) Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree. Journal of Statistical Mechanics: Theory and Experiment, 2014 (10). ISSN 1742-5468 http://dx.doi.org/10.1088/1742-5468/2014/10/P10031 doi:10.1088/1742-5468/2014/10/P10031 |
| spellingShingle | QA Mathematics QC Physics Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree |
| title | Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree |
| title_full | Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree |
| title_fullStr | Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree |
| title_full_unstemmed | Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree |
| title_short | Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree |
| title_sort | phase transition for the p-adic ising–vannimenus model on the cayley tree |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/1/mfmdha-JSTAT%282014%29.pdf http://irep.iium.edu.my/38902/4/38902_Phase%20transition_scopus_new.pdf |