On a factor associated with the unordered phase of \(\lambda\)-model on a Cayley tree

DOI10.1016/S0034-4877(04)90001-8zbMath1135.82305arXivmath/0411196MaRDI QIDQ1433684

Farrukh Mukhamedov

Publication date: 1 July 2004

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411196

zbMATH Keywords

von Neumann algebraCayley treeGibbs measureGNS construction\(\lambda\)-modelunordered phase

Mathematics Subject Classification ID

Applications of operator algebras to the sciences (47L90) Phase transitions (general) in equilibrium statistical mechanics (82B26) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Applications of functional analysis in statistical physics (46N55)

Related Items (17)

Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree ⋮ On ground states and phase transition for \(\lambda\)-model with the competing Potts interactions on Cayley trees ⋮ 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 ⋮ On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three ⋮ Weakly periodic ground states for the \(\lambda \)-model ⋮ On non-Archimedean recurrence equations and their applications ⋮ 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 ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ Ground states and phase transition of the \(\lambda\) model on the Cayley tree ⋮ Factors generated by \textit{XY}-model with competing Ising interactions on the Cayley tree ⋮ Renormalization method in \(p\)-adic \(\lambda\)-model on the Cayley tree ⋮ 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 ⋮ Phase transition of mixed type \(p\)-adic \({\lambda}\)-Ising model on Cayley tree ⋮ On \(P\)-adic \(\lambda\)-model on the Cayley tree. II: Phase transitions

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