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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2021 Volume 313, Pages 192–207 (Mi tm4180)
This article is cited in 8 papers

Quantum Markov Chains on Comb Graphs: Ising Model

Farrukh Mukhamedova, Abdessatar Souissibc, Tarek Hamdide

a Department of Mathematical Sciences, College of Science, United Arab Emirates University, 15551 Al Ain, United Arab Emirates
b Department of Accounting, College of Business Management, Qassim University, Ar Rass, Saudi Arabia
c Preparatory Institute for Scientific and Technical Studies, Carthage University, 1054, Amilcar, Tunisia
d Department of Management Information Systems, College of Business Management, Qassim University, Ar Rass, Saudi Arabia
e Laboratoire d'Analyse Mathématiques et Applications LR11ES11, Université de Tunis El-Manar, 2092, Tunis, Tunisia

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.

Keywords: quantum Markov chain, Ising model, comb graph, clustering.

UDC: 517.98

Received: May 16, 2020
Revised: October 15, 2020
Accepted: April 10, 2021

DOI: 10.4213/tm4180


 English version: Proceedings of the Steklov Institute of Mathematics, 2021, 313, 178–192

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© Steklov Math. Inst. of RAS, 2024