https://doi.org/10.1140/epjb/s10051-025-00905-6
Regular Article - Statistical and Nonlinear Physics
Mixed quantum Ising–XY model on a Cayley tree of order two
1
Department of Physics, College of Science, United Arab Emirates University, P.O. Box 15551, Al Ain, Abu Dhabi, UAE
2
Department of Mathematical Sciences, College of Science, United Arab Emirates University, P.O. Box 15551, Al Ain, Abu Dhabi, UAE
a farrukh.m@uaeu.ac.ae, far75m@gmail.com
Received:
9
January
2025
Accepted:
18
March
2025
Published online:
8
April
2025
This paper deals with a quantum Markov chain (QMC) associated with mixed quantum Ising–XY model on a Cayley tree of order two. The considered mixed model has the nearest-neighbor Ising interaction 
at odd levels of the tree, and the nearest-neighbor XY-interaction 
at even levels of the tree. It is known that for the nearest-neighbor Ising model on the Cayley tree, there occurs a phase transition. However, for the quantum XY model on the same tree there is unique quantum Markov chain. Therefore, it is natural to investigate the mixture of these models on the Cayley tree of order two. It turns out that for this mixed model there is only unique periodic QMC, which is a translation-invariant one. Moreover, one can construct non-translation-invariant QMC for the model.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
