On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the prese...
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Springer Netherlands
2016
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| Online Access: | http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/1/53490_On%20an%20Algebraic%20Propert.pdf http://irep.iium.edu.my/53490/2/53490_On%20an%20Algebraic%20Propert_WOS.pdf http://irep.iium.edu.my/53490/3/53490_On%20an%20Algebraic%20Propert_SCOPUS.pdf |
| _version_ | 1848784239197159424 |
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| author | Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar |
| author_facet | Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC’s on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains |
| first_indexed | 2025-11-14T16:34:05Z |
| format | Article |
| id | iium-53490 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T16:34:05Z |
| publishDate | 2016 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-534902017-10-21T07:33:58Z http://irep.iium.edu.my/53490/ On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar QA Mathematics QC Physics It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC’s on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains Springer Netherlands 2016-12 Article PeerReviewed application/pdf en http://irep.iium.edu.my/53490/1/53490_On%20an%20Algebraic%20Propert.pdf application/pdf en http://irep.iium.edu.my/53490/2/53490_On%20an%20Algebraic%20Propert_WOS.pdf application/pdf en http://irep.iium.edu.my/53490/3/53490_On%20an%20Algebraic%20Propert_SCOPUS.pdf Mukhamedov, Farrukh and Souissi, Abdessatar and Barhoumi, Abdessatar (2016) On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree. Mathematical Physics Analysis and Geometry, 19 (4). 21-1 -21-18. ISSN 1385-0172 E-ISSN 1572-9656 https://link.springer.com/article/10.1007/s11040-016-9225-x 10.1007/s11040-016-9225-x |
| spellingShingle | QA Mathematics QC Physics Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree |
| title | On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree |
| title_full | On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree |
| title_fullStr | On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree |
| title_full_unstemmed | On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree |
| title_short | On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree |
| title_sort | on an algebraic property of the disordered phase of the ising model with competing interactions on a cayley tree |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/1/53490_On%20an%20Algebraic%20Propert.pdf http://irep.iium.edu.my/53490/2/53490_On%20an%20Algebraic%20Propert_WOS.pdf http://irep.iium.edu.my/53490/3/53490_On%20an%20Algebraic%20Propert_SCOPUS.pdf |