MARKOVIAN KMS-STATES FOR ONE-DIMENSIONAL SPIN CHAINS

DOI10.1142/S0219025799000369zbMath1043.82506MaRDI QIDQ4810362

Volkmar Liebscher, Luigi Accardi

Publication date: 3 September 2004

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

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Applications of functional analysis in statistical physics (46N55)

Related Items (18)

Entropy of quantum Markov states on Cayley trees ⋮ Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree ⋮ MARKOV STATES AND CHAINS ON THE CAR ALGEBRA ⋮ Matrix analysis and quantum information ⋮ Non-homogeneous quantum Markov states and quantum Markov fields ⋮ On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three ⋮ FREE ENERGY DENSITY FOR MEAN FIELD PERTURBATION OF STATES OF A ONE-DIMENSIONAL SPIN CHAIN ⋮ FACTORS GENERATED BY C*-FINITELY CORRELATED STATES ⋮ On quantum Markov chains on Cayley tree. III: Ising model ⋮ Quantum Markov states on Cayley trees ⋮ Refinement of quantum Markov states on trees ⋮ A few remarks on mixing properties of \(C^*\)-dynamical systems ⋮ QUANTUM MARKOV FIELDS ON GRAPHS ⋮ Structure of sufficient quantum coarse-grainings ⋮ QUANTUM MARKOV FIELDS ⋮ WEAK AND STRONG MARTINGALE CONVERGENCES OF GENERALIZED CONDITIONAL EXPECTATIONS IN NONCOMMUTATIVE L^p-SPACES ⋮ 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

Cites Work

• Local perturbations of conditional expectations
• Conditional expectations in von Neumann algebras and a theorem of Takesaki
• Finitely correlated states on quantum spin chains
• Abundance of translation invariant pure states on quantum spin chains
• The noncommutative Markovian property
• Finitely correlated pure states
• Dynamical entropy of generalized quantum Markov chains
• Gibbsian random fields. The general case
• Conditional expectations in von Neumann algebras
• A Characterization of Pure Finitely Correlated States
• Prescribing a System of Random Variables by Conditional Distributions

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