Quantum Markov Chains on Comb Graphs: Ising Model

Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 languageEnglish
Pages (from-to)178-192
Number of pages15
JournalProceedings of the Steklov Institute of Mathematics
Issue number1
Publication statusPublished - Jul 2021


  • Ising model
  • clustering
  • comb graph
  • quantum Markov chain

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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