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Preprints Archive: Abstract of IC2010028 (2010)

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

by Farrukh Mukhamedov and Mansoor Saburov

Document info: Pages 34, Figures 1.

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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