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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 313, Pages 192–207
DOI: https://doi.org/10.4213/tm4180 (Mi tm4180) 		 
This article is cited in 8 scientific papers (total 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
Full-text PDF (254 kB) Citations (8)
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DOI: https://doi.org/10.4213/tm4180
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.
Funding agency Grant number
Qassim University cba-2019-2-2-I-5400
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.
Received: May 16, 2020
Revised: October 15, 2020
Accepted: April 10, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 313, Pages 178–192
DOI: https://doi.org/10.1134/S0081543821020176
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi, “Quantum Markov Chains on Comb Graphs: Ising Model”, Mathematics of Quantum Technologies, Collected papers, Trudy Mat. Inst. Steklova, 313, Steklov Math. Inst., Moscow, 2021, 192–207; Proc. Steklov Inst. Math., 313 (2021), 178–192
Citation in format AMSBIB
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\paper Quantum Markov Chains on Comb Graphs: Ising Model
\inbook Mathematics of Quantum Technologies
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 313
\pages 192--207
\publ Steklov Math. Inst.
\publaddr Moscow
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  • https://doi.org/10.4213/tm4180
  • https://www.mathnet.ru/eng/tm/v313/p192
    • This publication is cited in the following 8 articles:
    1. A. Souissi, F. Mukhamedov, A. Barhoumi, “Tree-homogeneous quantum Markov chains”, Int. J. Theor. Phys., 62:2 (2023), 19  crossref  mathscinet
    2. 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  crossref  mathscinet
    3. A. Souissi, E. G. Soueidy, M. Rhaima, “Clustering property for quantum Markov chains on the comb graph”, AIMS Mathematics, 8:4 (2023), 7865  crossref  mathscinet
    4. A. Souissi, “On stopping rules for tree-indexed quantum Markov chains”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 26:03 (2023), 2250030  crossref  mathscinet
    5. 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  crossref  mathscinet
    6. A. Barhoumi, A. Souissi, “Recurrence of a class of quantum Markov chains on trees”, Chaos, Solitons & Fractals, 164 (2022), 112644  crossref  mathscinet
    7. A. Souissi, F. Mukhamedov, “Entropy of quantum Markov states on Cayley trees”, J. Stat. Mech., 2022:9 (2022), 093101  crossref  mathscinet
    8. 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  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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