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arXiv · 2108.03924

Quantum Markov Chains on the Comb graphs: Ising model

Farrukh Mukhamedov·Abdessatar Souissi·Tarek Hamdi
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Abstract

In the present paper, we construct quantum Markov chains (QMC) over the Comb graphs. As an application of this construction, it is proved the existence of the disordered phase for the Ising type models (within QMC scheme) over the Comb graphs. Moreover, it is also established that the associated QMC has clustering property with respect to translations of the graph. We stress that this paper is the first one where a nontrivial example of QMC over non-regular graphs is given.

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Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi. 2021-08-09. Quantum Markov Chains on the Comb graphs: Ising model. https://doi.org/10.1134/s0081543821020176

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