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Types of factors generated by quantum Markov states of Ising model with competing interactions on the Cayley tree
Journal article   Peer reviewed

Types of factors generated by quantum Markov states of Ising model with competing interactions on the Cayley tree

Farrukh Mukhamedov and Abdessatar Souissi
Infinite dimensional analysis, quantum probability, and related topics, Vol.23(3), p.2050019
01/09/2020
DOI: https://doi.org/10.1142/S0219025720500198

Abstract

Mathematics Mathematics, Applied Physical Sciences Physics Physics, Mathematical Quantum Science & Technology Science & Technology Statistics & Probability
In this paper, we consider Quantum Markov States (QMS) corresponding to the Ising model with competing interactions on the Cayley tree of order two. Earlier, some algebraic properties of these states were investigated. In this paper, we prove that if the competing interaction is rational then the von Neumann algebra, corresponding to the QMS associated with disordered phase of the model, has type IIIlambda, lambda is an element of (0, 1).

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