Quantum phase transition for Ising type models on a Cayley tree of order two

In this work, we construct a quantum Markov chain (QMC) associated by the classical Ising model with competing interactions on the Cayley tree of order two. In the construction QMC is defined as a weak limit of finite volume states on quasi-local algebras with boundary conditions. We point out tha...

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Main Authors:	Mukhamedov, Farrukh, Barhoumi, Abdessatar, Soussi, Abdessatar
Format:	Conference or Workshop Item
Language:	English English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/38019/ http://irep.iium.edu.my/38019/1/Farrukh.pdf http://irep.iium.edu.my/38019/4/ppt_Faruukh.pdf

id	iium-38019
recordtype	eprints
spelling	iium-380192018-06-19T02:38:15Z http://irep.iium.edu.my/38019/ Quantum phase transition for Ising type models on a Cayley tree of order two Mukhamedov, Farrukh Barhoumi, Abdessatar Soussi, Abdessatar QA Mathematics In this work, we construct a quantum Markov chain (QMC) associated by the classical Ising model with competing interactions on the Cayley tree of order two. In the construction QMC is defined as a weak limit of finite volume states on quasi-local algebras with boundary conditions. We point out that phase transitions in a quantum setting play an important role to understand quantum spin systems We have defined a notion of phase transition in QMC scheme. Namely, such a notion is based on the quasi-equivalence of QMC. Therefore, such a phase transition is purely non-commutative. In this work we establish the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out that the found critical temperature coincides with usual critical temperature. 2014-08-23 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/38019/1/Farrukh.pdf application/pdf en http://irep.iium.edu.my/38019/4/ppt_Faruukh.pdf Mukhamedov, Farrukh and Barhoumi, Abdessatar and Soussi, Abdessatar (2014) Quantum phase transition for Ising type models on a Cayley tree of order two. In: 35th International Conference on Quantum Probability and Related Topics (QP35), 22-26 August 2014, Korea.
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QA Mathematics
spellingShingle	QA Mathematics Mukhamedov, Farrukh Barhoumi, Abdessatar Soussi, Abdessatar Quantum phase transition for Ising type models on a Cayley tree of order two
description	In this work, we construct a quantum Markov chain (QMC) associated by the classical Ising model with competing interactions on the Cayley tree of order two. In the construction QMC is defined as a weak limit of finite volume states on quasi-local algebras with boundary conditions. We point out that phase transitions in a quantum setting play an important role to understand quantum spin systems We have defined a notion of phase transition in QMC scheme. Namely, such a notion is based on the quasi-equivalence of QMC. Therefore, such a phase transition is purely non-commutative. In this work we establish the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out that the found critical temperature coincides with usual critical temperature.
format	Conference or Workshop Item
author	Mukhamedov, Farrukh Barhoumi, Abdessatar Soussi, Abdessatar
author_facet	Mukhamedov, Farrukh Barhoumi, Abdessatar Soussi, Abdessatar
author_sort	Mukhamedov, Farrukh
title	Quantum phase transition for Ising type models on a Cayley tree of order two
title_short	Quantum phase transition for Ising type models on a Cayley tree of order two
title_full	Quantum phase transition for Ising type models on a Cayley tree of order two
title_fullStr	Quantum phase transition for Ising type models on a Cayley tree of order two
title_full_unstemmed	Quantum phase transition for Ising type models on a Cayley tree of order two
title_sort	quantum phase transition for ising type models on a cayley tree of order two
publishDate	2014
url	http://irep.iium.edu.my/38019/ http://irep.iium.edu.my/38019/1/Farrukh.pdf http://irep.iium.edu.my/38019/4/ppt_Faruukh.pdf
first_indexed	2023-09-18T20:54:33Z
last_indexed	2023-09-18T20:54:33Z
_version_	1777410216836464640

Quantum phase transition for Ising type models on a Cayley tree of order two

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