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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2014
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my.iium.irep.38019 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. |
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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/38019/1/Farrukh.pdf http://irep.iium.edu.my/38019/4/ppt_Faruukh.pdf http://irep.iium.edu.my/38019/ |
| _version_ |
1643616687617998848 |
| score |
13.251813 |