Phase transitions for XY-model on the Cayley tree of order three in quantum Markov chain scheme
In the present Note 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 the Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2011
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/1611/ http://irep.iium.edu.my/1611/ http://irep.iium.edu.my/1611/ http://irep.iium.edu.my/1611/1/mfms-CRM%282011%29.pdf |
| Summary: | In the present Note 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 the 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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