On Quantum Markov Chains on Cayley Tree II: Phase Transitions for the Associated Chain with XY-Model on the Cayley Tree of Order Three

Luigi Accardi, Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

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 distinct QMC for the given family of interaction operators {K 〈x,y〉}.

Original languageEnglish
Pages (from-to)1109-1144
Number of pages36
JournalAnnales Henri Poincare
Volume12
Issue number6
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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