On an algebraic property of the disordered phase of the Ising model with competing interactions on a Cayley tree

DOI10.1007/s11040-016-9225-xzbMath1413.46060OpenAlexW2530741748MaRDI QIDQ1663432

Farrukh Mukhamedov, Abdessatar Barhoumi, Abdessatar Souissi

Publication date: 21 August 2018

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

Full work available at URL: https://doi.org/10.1007/s11040-016-9225-x

zbMATH Keywords

Cayley treecompeting interactiondisordered phasequantum Markov chainquasi-equivalenceIsing-type model

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) Measures of information, entropy (94A17) Markov processes (60J99)

Related Items (16)

Entropy of quantum Markov states on Cayley trees ⋮ 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 ⋮ Absolute continuity of non-homogeneous Gibbs measures of the Ising model on the Cayley tree ⋮ 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 ⋮ 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 ⋮ 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree
• On quantum Markov chains on Cayley tree. III: Ising model
• On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three
• Uniqueness of quantum Markov chains associated with an \(XY\)-model on a Cayley tree of order 2
• Extremity of the disordered phase in the Ising model on the Bethe lattice
• On Ising model with four competing interactions on Cayley tree
• Conditional expectations in von Neumann algebras and a theorem of Takesaki
• 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
• Non-homogeneous quantum Markov states and quantum Markov fields
• On a factor associated with the unordered phase of \(\lambda\)-model on a Cayley tree
• Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice
• On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras
• Reconstruction on trees: Beating the second eigenvalue
• On the extremality of the disordered state for the Ising model on the Bethe lattice
• New phase transitions of the Ising model on Cayley trees
• On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras. II
• Gibbs Measures on Cayley Trees
• QUANTUM MARKOV FIELDS
• ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO
• QUANTUM MARKOV FIELDS ON GRAPHS
• Gibbs States on Countable Sets
• A Characterization of Pure Finitely Correlated States
• MARKOV STATES AND CHAINS ON THE CAR ALGEBRA

This page was built for publication: On an algebraic property of the disordered phase of the Ising model with competing interactions on a Cayley tree