Transitions de phases pour un modèle XY sur un arbre de Cayley d'ordre trois dans un schéma de chaines de Markov quantiques

Farrukh Mukhamedov; Mansoor Saburov

doi:10.1016/j.crma.2011.02.010

Transitions de phases pour un modèle XY sur un arbre de Cayley d'ordre trois dans un schéma de chaines de Markov quantiques

Translated title of the contribution: Phase transitions for XY-model on the Cayley tree of order three in quantum Markov chain scheme

Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In the present Note 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 the 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〉}.

Translated title of the contribution	Phase transitions for XY-model on the Cayley tree of order three in quantum Markov chain scheme
Original language	French
Pages (from-to)	425-428
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	7-8
DOIs	https://doi.org/10.1016/j.crma.2011.02.010
Publication status	Published - Apr 2011
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2011.02.010

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title = "Transitions de phases pour un mod{\`e}le XY sur un arbre de Cayley d'ordre trois dans un sch{\'e}ma de chaines de Markov quantiques",

abstract = "In the present Note 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 the 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〉\}.",

author = "Farrukh Mukhamedov and Mansoor Saburov",

year = "2011",

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doi = "10.1016/j.crma.2011.02.010",

language = "French",

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journal = "Comptes Rendus Mathematique",

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AU - Saburov, Mansoor

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Y1 - 2011/4

N2 - In the present Note 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 the 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 Note 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 the 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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Transitions de phases pour un modèle XY sur un arbre de Cayley d'ordre trois dans un schéma de chaines de Markov quantiques

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