On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree
In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY -model on a Cayle...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Birkhaeuser Verlag AG
2011
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/1817/ http://irep.iium.edu.my/1817/ http://irep.iium.edu.my/1817/ http://irep.iium.edu.my/1817/1/acmfms-AHP%282011%29.pdf |
| Summary: | In the present paper, we study forward quantum Markov chains
(QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY -model on a Cayley tree of order three in QMC scheme. By the phase
transition we mean the existence of two distinct QMC for the given family of interaction operators {K_{x,y}}. |
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