On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree

• Main Authors: Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor
• Format: Article
• Language: English
• Published: Birkhaeuser Verlag AG 2011
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/1817/1/acmfms-AHP%282011%29.pdf; http://irep.iium.edu.my/1817/; http://link.springer.com/article/10.1007%2Fs00023-011-0107-2
• Institution: Universiti Islam Antarabangsa Malaysia

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 Cayle...