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

Farrukh Mukhamedov, Abdessatar Souissi

Research output: Contribution to journalArticlepeer-review

3 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 languageEnglish
Article number2050019
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume23
Issue number3
DOIs
Publication statusPublished - Sep 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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