Clustering property of quantum Markov chain associated to XY-model with competing Ising interactions on the Cayley tree of order two

DOI10.1007/S11040-019-9308-6zbMath1421.46044OpenAlexW2921828461WikidataQ128231738 ScholiaQ128231738MaRDI QIDQ1741774

Soueidy El Gheteb, Farrukh Mukhamedov

Publication date: 7 May 2019

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11040-019-9308-6

zbMATH Keywords

uniquenessCayley treeXY modelcompeting interactionquantum Markov chainclustering property

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) 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) Markov processes (60J99)

Related Items (13)

Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions ⋮ Diagonalizability of quantum Markov states on trees ⋮ On stopping rules for tree-indexed quantum Markov chains ⋮ Recurrence of a class of quantum Markov chains on trees ⋮ Nonlinear stochastic operators and associated inhomogeneous entangled quantum Markov chains ⋮ On a \(\psi\)-mixing property for entangled Markov chains ⋮ Tree-homogeneous quantum Markov chains ⋮ A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree ⋮ Types of factors generated by quantum Markov states of Ising model with competing interactions on the Cayley tree ⋮ Refinement of quantum Markov states on trees ⋮ Factors generated by \textit{XY}-model with competing Ising interactions on the Cayley tree ⋮ Quantum Markov chains on comb graphs: Ising model ⋮ A Class of Quantum Markov Fields on Tree-like Graphs: Ising-type Model on a Husimi Tree

Cites Work

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• QUANTUM MARKOV FIELDS ON GRAPHS
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