TY - JOUR
T1 - On Quantum Markov Chains on Cayley Tree II
T2 - Phase Transitions for the Associated Chain with XY-Model on the Cayley Tree of Order Three
AU - Accardi, Luigi
AU - Mukhamedov, Farrukh
AU - Saburov, Mansoor
N1 - Funding Information:
The present study has been done within the grant FRGS0308-91 of Malaysian Ministry of Higher Education. The authors also acknowledge the MOSTI grant 01-01-08-SF0079. This work was done while the second named author (F.M.) was visiting the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, as a Junior Associate. He would like to thank the Centre for hospitality and financial support.
PY - 2011/9
Y1 - 2011/9
N2 - 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〉}.
AB - 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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U2 - 10.1007/s00023-011-0107-2
DO - 10.1007/s00023-011-0107-2
M3 - Article
AN - SCOPUS:79961025087
SN - 1424-0637
VL - 12
SP - 1109
EP - 1144
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 6
ER -