Phase transitions for XY-model on the Cayley tree of order three in quantum Markov chain scheme

Mukhamedov, Farrukh and Saburov, Mansoor (2011) Phase transitions for XY-model on the Cayley tree of order three in quantum Markov chain scheme. Comptes Rendus Mathematique, 349 (7-8). pp. 425-428. ISSN 1631 - 073X

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Abstract

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}}.

Item Type:	Article (Journal)
Additional Information:	5537/1611
Uncontrolled Keywords:	Quantum Markov Chains (QMC), Cayley tree
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	05 Sep 2011 15:54
Last Modified:	05 Sep 2011 15:54
URI:	http://irep.iium.edu.my/id/eprint/1611

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