Luigi Accardi, Farrukh Mukhamedov, Mansoor Saburov
Published 2010-04-21, updated 2010-10-18Version 2
In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction we investigate QMC associated with XY-model on a Caylay tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.
Comments: 19 pages
Journal: Infinite Dim. Anal. Quantum Probab. Related Topics Vol. 14, No. 3 (2011) 443--463
On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three
Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley tree
On Uniqueness of Gibbs Measures for $P$-Adic Nonhomogeneous $ł$-Model on the Cayley Tree
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