Phase transitions for quantum Markov chains associated with ising type models on a Cayley tree
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing AG
2016
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/50295/ http://irep.iium.edu.my/50295/ http://irep.iium.edu.my/50295/1/mfabas-JSP%282016%29.pdf |
| Summary: | The main aim of the present paper is to prove the existence of a phase transition
in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note
that this kind of models do not have one-dimensional analogous, i.e. the considered model
persists only on trees. In this paper, we provide a more general construction of forward
QMC. In that construction, a QMC is defined as a weak limit of finite volume states with
boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states
the existence of a phase transition for the Ising model with competing interactions on aCayley
tree of order two. By the phase transition we mean the existence of two distinct QMC which
are not quasi-equivalent and their supports do not overlap. We also study some algebraic
property of the disordered phase of the model, which is a new phenomena even in a classical
setting. |
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