QUANTUM MARKOV FIELDS ON GRAPHS

DOI10.1142/S0219025710004000zbMath1211.46072arXiv0911.1667MaRDI QIDQ3580205

Hiromichi Ohno, Luigi Accardi, Farrukh Mukhamedov

Publication date: 11 August 2010

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.1667

zbMATH Keywords

graphCayley tree\(d\)-Markov chainsentangled Markov fieldsgeneralized Markov state

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) Measures of information, entropy (94A17) Markov processes (60J99)

Related Items (22)

Entropy of quantum Markov states on Cayley trees ⋮ Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions ⋮ Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree ⋮ On an algebraic property of the disordered phase of the Ising model with competing interactions on a Cayley tree ⋮ Diagonalizability of quantum Markov states on trees ⋮ Open quantum random walks and quantum Markov chains on trees. II: The recurrence ⋮ Tree-homogeneous quantum Markov chains ⋮ On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three ⋮ On quantum Markov chains on Cayley tree. III: Ising model ⋮ A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree ⋮ Quantum Markov states on Cayley trees ⋮ Types of factors generated by quantum Markov states of Ising model with competing interactions on the Cayley tree ⋮ Clustering property of quantum Markov chain associated to XY-model with competing Ising interactions on the Cayley tree of order two ⋮ Refinement of quantum Markov states on trees ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ Phase transitions for \(XY\)-model on the Cayley tree of order three in quantum Markov chain scheme ⋮ Factors generated by \textit{XY}-model with competing Ising interactions on the Cayley tree ⋮ Quantum Markov chains on comb graphs: Ising model ⋮ ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO ⋮ Uniqueness of quantum Markov chains associated with an \(XY\)-model on a Cayley tree of order 2 ⋮ A Class of Quantum Markov Fields on Tree-like Graphs: Ising-type Model on a Husimi Tree ⋮ Block Markov chains on trees

Cites Work

• Countable state space Markov random fields and Markov chains on trees
• Construction of a Markov field on an infinite tree
• Bounded, attractive and repulsive Markov specifications on trees and on the one-dimensional lattice
• Finitely correlated states on quantum spin chains
• Ground states of VBS models on Cayley trees
• Markov random fields on an infinite tree
• The noncommutative Markovian property
• Entangled Markov chains
• QUANTUM MARKOV FIELDS
• Gibbs States on Countable Sets
• MARKOVIAN KMS-STATES FOR ONE-DIMENSIONAL SPIN CHAINS
• MARKOV STATES AND CHAINS ON THE CAR ALGEBRA
• ENTANGLED MARKOV CHAINS ARE INDEED ENTANGLED
• ENTANGLED MARKOV CHAINS GENERATED BY SYMMETRIC CHANNELS

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