TY - JOUR
T1 - On Translation Invariant Quantum Markov Chains associated with Ising-XY models on a Cayley tree
AU - Mukhamedov, Farrukh
AU - Barhoumi, Abdessatar
AU - Souissi, Abdessatar
AU - El Gheteb, Soueidy
N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.
PY - 2017/4/3
Y1 - 2017/4/3
N2 - In this paper, we consider the Ising-XY model with competing interactions on the Cayley tree of order two. This model can be seen as a non-commutative (i.e. J-XY -interactions on next-neighbor vertices) perturbation of the classical Ising model on the Cayley tree. For the considered model we establish the existence of three translation-invariant quantum Markov chains. We notice that if the XY -interactions vanish, i.e. J = 0, then one gets the Ising model. If the classical Ising model vanishes in the considered model, then we obtain XY -model for which it turns out there exists only one translation invariant QMC.
AB - In this paper, we consider the Ising-XY model with competing interactions on the Cayley tree of order two. This model can be seen as a non-commutative (i.e. J-XY -interactions on next-neighbor vertices) perturbation of the classical Ising model on the Cayley tree. For the considered model we establish the existence of three translation-invariant quantum Markov chains. We notice that if the XY -interactions vanish, i.e. J = 0, then one gets the Ising model. If the classical Ising model vanishes in the considered model, then we obtain XY -model for which it turns out there exists only one translation invariant QMC.
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U2 - 10.1088/1742-6596/819/1/012006
DO - 10.1088/1742-6596/819/1/012006
M3 - Conference article
AN - SCOPUS:85018755500
SN - 1742-6588
VL - 819
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012006
T2 - 37th International Conference on Quantum Probability and Related Topics, QP 2016
Y2 - 22 August 2016 through 26 August 2016
ER -