Quantum Markov chains on comb graphs: Ising model. (English. Russian original) Zbl 1469.82011
Proc. Steklov Inst. Math. 313, 178-192 (2021); translation from Tr. Mat. Inst. Steklova 313, 192-207 (2021).
Summary: 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.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 05C99 | Graph theory |
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