Abstract:
We construct quantum Markov chains (QMCs) over comb graphs. As an application of this construction, we prove the existence of a disordered phase for Ising type models (within the QMC scheme) over comb graphs. Moreover, we also establish that the associated QMC has the clustering property with respect to translations of the graph. We stress that this paper is the first one where a nontrivial example of QMCs over irregular graphs is given.
The authors gratefully acknowledge Qassim University, represented by the Deanship of Scientific Research, for the financial support of this research (no. cba-2019-2-2-I-5400) during the academic year 1440 AH / 2019 AD.
This publication is cited in the following 8 articles:
A. Souissi, F. Mukhamedov, A. Barhoumi, “Tree-homogeneous quantum Markov chains”, Int. J. Theor. Phys., 62:2 (2023), 19
L. Accardi, A. Andolsi, F. Mukhamedov, M. Rhaima, A. Souissi, “Clustering quantum Markov chains on trees associated with open quantum random walks”, AIMS Mathematics, 8:10 (2023), 23003
A. Souissi, E. G. Soueidy, M. Rhaima, “Clustering property for quantum Markov chains on the comb graph”, AIMS Mathematics, 8:4 (2023), 7865
A. Souissi, “On stopping rules for tree-indexed quantum Markov chains”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 26:03 (2023), 2250030
A. Souissi, E. G. Soueidy, A. Barhoumi, “On a ψ-mixing property for Entangled Markov Chains”, Physica A: Statistical Mechanics and its Applications, 613 (2023), 128533
A. Barhoumi, A. Souissi, “Recurrence of a class of quantum Markov chains on trees”, Chaos, Solitons & Fractals, 164 (2022), 112644
A. Souissi, F. Mukhamedov, “Entropy of quantum Markov states on Cayley trees”, J. Stat. Mech., 2022:9 (2022), 093101
Souissi A., “A Class of Quantum Markov Fields on Tree-Like Graphs: Ising-Type Model on a Husimi Tree”, Open Syst. Inf. Dyn., 28:01 (2021), 2150004