Quantum Markov Chains on Comb Graphs: Ising Model

Farrukh Mukhamedov; Abdessatar Souissi; Tarek Hamdi

doi:10.1134/S0081543821020176

Quantum Markov Chains on Comb Graphs: Ising Model

Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	178-192
Number of pages	15
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	313
Issue number	1
DOIs	https://doi.org/10.1134/S0081543821020176
Publication status	Published - Jul 2021

Keywords

clustering
comb graph
Ising model
quantum Markov chain

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1134/S0081543821020176

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title = "Quantum Markov Chains on Comb Graphs: Ising Model",

abstract = "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 = "clustering, comb graph, Ising model, quantum Markov chain",

author = "Farrukh Mukhamedov and Abdessatar Souissi and Tarek Hamdi",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = jul,

doi = "10.1134/S0081543821020176",

language = "English",

volume = "313",

pages = "178--192",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

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TY - JOUR

T1 - Quantum Markov Chains on Comb Graphs

T2 - Ising Model

AU - Mukhamedov, Farrukh

AU - Souissi, Abdessatar

AU - Hamdi, Tarek

N1 - Funding Information: 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. Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - clustering

KW - comb graph

KW - Ising model

KW - quantum Markov chain

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DO - 10.1134/S0081543821020176

M3 - Article

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VL - 313

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EP - 192

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

IS - 1

ER -

Quantum Markov Chains on Comb Graphs: Ising Model

Abstract

Keywords

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