Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree

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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Main Authors: Mukhamedov, Farrukh, Barhoumi, Abdessatar, Souissi, Abdessatar
Format: Article
Language:English
Published: Springer International Publishing AG 2016
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/50295/
http://irep.iium.edu.my/50295/
http://irep.iium.edu.my/50295/1/mfabas-JSP%282016%29.pdf
id iium-50295
recordtype eprints
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
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Mukhamedov, Farrukh
Barhoumi, Abdessatar
Souissi, Abdessatar
Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree
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.
format Article
author Mukhamedov, Farrukh
Barhoumi, Abdessatar
Souissi, Abdessatar
author_facet Mukhamedov, Farrukh
Barhoumi, Abdessatar
Souissi, Abdessatar
author_sort Mukhamedov, Farrukh
title 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_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_sort phase transitions for quantum markov chains associated with ising type models on a cayley tree
publisher Springer International Publishing AG
publishDate 2016
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
first_indexed 2023-09-18T21:11:05Z
last_indexed 2023-09-18T21:11:05Z
_version_ 1777411257280757760

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