caa a22 4500 445320206 CHVBK 20180317142701.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00023-011-0107-2 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0107-2 On Quantum Markov Chains on Cayley Tree II: Phase Transitions for the Associated Chain with XY -Model on the Cayley Tree of Order Three [Elektronische Daten] [Luigi Accardi, Farrukh Mukhamedov, Mansoor Saburov] 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 $${\{K_{\langle x,y\rangle}\}}$$ . Springer Basel AG, 2011 Accardi Luigi Centro Interdisciplinare Vito Volterra, II Università di Roma "Tor Vergata”, Via Columbia 2, 00133, Rome, Italy aut Mukhamedov Farrukh Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P. O. Box 141, 25710, Kuantan, Pahang, Malaysia aut Saburov Mansoor Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P. O. Box 141, 25710, Kuantan, Pahang, Malaysia aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/6(2011-09-01), 1109-1144 1424-0637 12:6<1109 2011 12 23 https://doi.org/10.1007/s00023-011-0107-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0107-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Accardi Luigi Centro Interdisciplinare Vito Volterra, II Università di Roma "Tor Vergata”, Via Columbia 2, 00133, Rome, Italy aut NATIONALLICENCE 700 1- Mukhamedov Farrukh Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P. O. Box 141, 25710, Kuantan, Pahang, Malaysia aut NATIONALLICENCE 700 1- Saburov Mansoor Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P. O. Box 141, 25710, Kuantan, Pahang, Malaysia aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/6(2011-09-01), 1109-1144 1424-0637 12:6<1109 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer