TY - JOUR
T1 - Types of factors generated by quantum Markov states of Ising model with competing interactions on the Cayley tree
AU - Mukhamedov, Farrukh
AU - Souissi, Abdessatar
N1 - Funding Information:
The first named author (F.M.) thanks the UAEU UPAR Grant No. G0003247 (Fund No. 31S391).
Publisher Copyright:
© 2020 World Scientific Publishing Company.
PY - 2020/9
Y1 - 2020/9
N2 - 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).
AB - 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).
KW - Cayley tree
KW - Ising model
KW - Quantum Markov state
KW - competing interaction
KW - von Neumann algebra
UR - http://www.scopus.com/inward/record.url?scp=85097422596&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85097422596&partnerID=8YFLogxK
U2 - 10.1142/S0219025720500198
DO - 10.1142/S0219025720500198
M3 - Article
AN - SCOPUS:85097422596
SN - 0219-0257
VL - 23
JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics
JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics
IS - 3
M1 - 2050019
ER -