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.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - Apr 3 2017|
|Event||37th International Conference on Quantum Probability and Related Topics, QP 2016 - Kuantan, Malaysia|
Duration: Aug 22 2016 → Aug 26 2016
ASJC Scopus subject areas
- Physics and Astronomy(all)