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

Farrukh Mukhamedov; Abdessatar Souissi

doi:10.1142/S0219025720500198

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

Farrukh Mukhamedov, Abdessatar Souissi

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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 IIIλ, λ ∈ (0, 1).

Original language	English
Article number	2050019
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	23
Issue number	3
DOIs	https://doi.org/10.1142/S0219025720500198
Publication status	Published - Sept 2020

Keywords

Cayley tree
Ising model
Quantum Markov state
competing interaction
von Neumann algebra

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

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10.1142/S0219025720500198

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KW - competing interaction

KW - von Neumann algebra

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

Abstract

Keywords

ASJC Scopus subject areas

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