TY - JOUR
T1 - Factors Generated by XY-Model with Competing Ising Interactions on the Cayley Tree
AU - Mukhamedov, Farrukh
AU - Gheteb, Soueidy El
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - In the present paper, we consider a quantum Markov chain corresponding to the XY-model with competing Ising interactions on the Cayley tree of order two. Earlier, it was proved that this state does exist and is unique. Moreover, it has clustering property. This means that the von Neumann algebra generated by this state is a factor. In the present paper, we establish that the factor generated by this state may have type III λλ∈ (0 , 1) which is unusual for states associated with models with nontrivial interactions.
AB - In the present paper, we consider a quantum Markov chain corresponding to the XY-model with competing Ising interactions on the Cayley tree of order two. Earlier, it was proved that this state does exist and is unique. Moreover, it has clustering property. This means that the von Neumann algebra generated by this state is a factor. In the present paper, we establish that the factor generated by this state may have type III λλ∈ (0 , 1) which is unusual for states associated with models with nontrivial interactions.
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U2 - 10.1007/s00023-019-00853-9
DO - 10.1007/s00023-019-00853-9
M3 - Article
AN - SCOPUS:85074133661
SN - 1424-0637
VL - 21
SP - 241
EP - 253
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 1
ER -