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

Access to Document

10.1016/j.crma.2011.02.010

Cite this

@article{5ede8d67503046e0a03ffd5c95f9ae14,

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",

month = apr,

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

language = "French",

volume = "349",

pages = "425--428",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Academie des sciences",

number = "7-8",

}

TY - JOUR

T1 - Transitions de phases pour un modèle XY sur un arbre de Cayley d'ordre trois dans un schéma de chaines de Markov quantiques

AU - Mukhamedov, Farrukh

AU - Saburov, Mansoor

PY - 2011/4

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〉}.

UR - http://www.scopus.com/inward/record.url?scp=79954887052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954887052&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2011.02.010

DO - 10.1016/j.crma.2011.02.010

M3 - Article

AN - SCOPUS:79954887052

SN - 1631-073X

VL - 349

SP - 425

EP - 428

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 7-8

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this