Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper,...
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| Format: | Article |
| Language: | English |
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Springer International Publishing AG
2016
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| Online Access: | http://irep.iium.edu.my/50295/ http://irep.iium.edu.my/50295/1/mfabas-JSP%282016%29.pdf |
| _version_ | 1848783615440191488 |
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| author | Mukhamedov, Farrukh Barhoumi, Abdessatar Souissi, Abdessatar |
| author_facet | Mukhamedov, Farrukh Barhoumi, Abdessatar Souissi, Abdessatar |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | The main aim of the present paper is to prove the existence of a phase transition
in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note
that this kind of models do not have one-dimensional analogous, i.e. the considered model
persists only on trees. In this paper, we provide a more general construction of forward
QMC. In that construction, a QMC is defined as a weak limit of finite volume states with
boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states
the existence of a phase transition for the Ising model with competing interactions on aCayley
tree of order two. By the phase transition we mean the existence of two distinct QMC which
are not quasi-equivalent and their supports do not overlap. We also study some algebraic
property of the disordered phase of the model, which is a new phenomena even in a classical
setting. |
| first_indexed | 2025-11-14T16:24:10Z |
| format | Article |
| id | iium-50295 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:24:10Z |
| publishDate | 2016 |
| publisher | Springer International Publishing AG |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-502952017-01-06T00:29:22Z http://irep.iium.edu.my/50295/ Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree Mukhamedov, Farrukh Barhoumi, Abdessatar Souissi, Abdessatar QA Mathematics The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on aCayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting. Springer International Publishing AG 2016-05 Article PeerReviewed application/pdf en http://irep.iium.edu.my/50295/1/mfabas-JSP%282016%29.pdf Mukhamedov, Farrukh and Barhoumi, Abdessatar and Souissi, Abdessatar (2016) Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree. Journal of Statistical Physics, 163 (3). pp. 544-567. ISSN 0022-4715 E-ISSN 1572-9613 (In Press) http://link.springer.com/article/10.1007/s10955-016-1495-y |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Barhoumi, Abdessatar Souissi, Abdessatar Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree |
| title | Phase transitions for quantum Markov chains
associated with ising type models on a Cayley tree |
| title_full | Phase transitions for quantum Markov chains
associated with ising type models on a Cayley tree |
| title_fullStr | Phase transitions for quantum Markov chains
associated with ising type models on a Cayley tree |
| title_full_unstemmed | Phase transitions for quantum Markov chains
associated with ising type models on a Cayley tree |
| title_short | Phase transitions for quantum Markov chains
associated with ising type models on a Cayley tree |
| title_sort | phase transitions for quantum markov chains
associated with ising type models on a cayley tree |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/50295/ http://irep.iium.edu.my/50295/ http://irep.iium.edu.my/50295/1/mfabas-JSP%282016%29.pdf |