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

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...

Full description

Bibliographic Details
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

Similar Items