Quantum Markov Chains on the Comb graphs: Ising model

TL;DR

This paper constructs quantum Markov chains on Comb graphs and demonstrates the existence of disordered phases for Ising models within this framework, highlighting a novel example on non-regular graphs.

Contribution

It introduces the first nontrivial quantum Markov chain example on non-regular graphs and analyzes phase behavior and clustering properties for Ising models.

Findings

Existence of disordered phase in QMC over Comb graphs

QMC exhibits clustering property with respect to graph translations

First example of QMC on non-regular graphs

Abstract

In the present paper, we construct quantum Markov chains (QMC) over the Comb graphs. As an application of this construction, it is proved the existence of the disordered phase for the Ising type models (within QMC scheme) over the Comb graphs. Moreover, it is also established that the associated QMC has clustering property with respect to translations of the graph. We stress that this paper is the first one where a nontrivial example of QMC over non-regular graphs is given.