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...
| Main Authors: | , , |
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| Format: | Proceeding Paper |
| Language: | English English |
| Published: |
2014
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/38019/1/Farrukh.pdf http://irep.iium.edu.my/38019/4/ppt_Faruukh.pdf |
| _version_ | 1796878969826443264 |
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| author | Mukhamedov, Farrukh Barhoumi, Abdessatar Soussi, Abdessatar |
| author_facet | Mukhamedov, Farrukh Barhoumi, Abdessatar Soussi, Abdessatar |
| author_sort | Mukhamedov, Farrukh |
| collection | IIUM |
| 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. |
| first_indexed | 2024-03-05T23:28:55Z |
| format | Proceeding Paper |
| id | oai:generic.eprints.org:38019 |
| institution | International Islamic University Malaysia |
| language | English English |
| last_indexed | 2024-03-05T23:28:55Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oai:generic.eprints.org: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 Proceeding Paper 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. |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Barhoumi, Abdessatar Soussi, Abdessatar Quantum phase transition for Ising type models on a Cayley tree of order two |
| title | 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_short | 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 |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/38019/1/Farrukh.pdf http://irep.iium.edu.my/38019/4/ppt_Faruukh.pdf |
| work_keys_str_mv | AT mukhamedovfarrukh quantumphasetransitionforisingtypemodelsonacayleytreeofordertwo AT barhoumiabdessatar quantumphasetransitionforisingtypemodelsonacayleytreeofordertwo AT soussiabdessatar quantumphasetransitionforisingtypemodelsonacayleytreeofordertwo |