Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley tree
Abstract
The main aim of the present paper is to establish the existence of a phase transition for the quantum Ising model with competing XY interactions within the quantum Markov chain (QMC) scheme. In this scheme, we employ the -algebraic approach to the phase transition problem. Note that these kinde of models do not have one-dimensional analogues, i.e. the considered model persists only on trees. It turns out that if the Ising part interactions vanish then the model with only competing XY -interactions on the Cayley tree of order two does not have a phase transition. By phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. Moreover, it is also shown that the QMC associated with the model have clustering property which implies that the von Neumann algebras corresponding to the states are factors.
Keywords
Cite
@article{arxiv.1902.03226,
title = {Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley tree},
author = {Farrukh Mukhamedov and Abdessatar Barhoumi and Abdessatar Souissi and Soueidy EL Gheteb},
journal= {arXiv preprint arXiv:1902.03226},
year = {2020}
}
Comments
30 pages. arXiv admin note: substantial text overlap with arXiv:1605.04546; text overlap with arXiv:cond-mat/0401295 by other authors