On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three

Abstract

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 now quasi equivalent QMC for the given family of interaction operators $\{K_{<x,y>}\}$.

34 pages, 1 figure

References in corpus (2)

• Quantum Markov fields on graphs
• On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two

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• Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
• Refinement of quantum Markov states on trees
• Quantum Markov Chains on the Comb graphs: Ising model