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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| 主要な著者: | , , |
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| フォーマット: | Conference or Workshop Item |
| 言語: | English English |
| 出版事項: |
2014
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| 主題: | |
| オンライン･アクセス: | 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/ |
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| 要約: | 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. |
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