Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree

DOI10.1007/s10955-016-1495-yzbMath1348.82034arXiv1605.04546OpenAlexW2299953410MaRDI QIDQ300601

Abdessatar Barhoumi, Abdessatar Souissi, Farrukh Mukhamedov

Publication date: 28 June 2016

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04546

zbMATH Keywords

phase transitionCayley treecompeting interactiondisordered phaseIsing type modelquantum Markov chainquasi-equivalence

Mathematics Subject Classification ID

Trees (05C05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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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, On stopping rules for tree-indexed quantum Markov chains, Recurrence of a class of quantum Markov chains on trees, Open quantum random walks and quantum Markov chains on trees. II: The recurrence, 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, 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

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