Quantum Markov Chains on Comb Graphs: Ising Model

Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)178-192
Number of pages15
JournalProceedings of the Steklov Institute of Mathematics
Volume313
Issue number1
DOIs
Publication statusPublished - Jul 2021

Keywords

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

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Fingerprint

Dive into the research topics of 'Quantum Markov Chains on Comb Graphs: Ising Model'. Together they form a unique fingerprint.

Cite this