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.

中文翻译：

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梳状图上的量子马尔可夫链：Ising 模型

摘要

我们在梳状图上构建量子马尔可夫链（QMC）。作为这种构造的应用，我们证明了梳状图上 Ising 类型模型（在 QMC 方案内）的无序相的存在。此外，我们还确定关联的 QMC 具有关于图平移的聚类特性。我们强调，这篇论文是第一个给出不规则图上 QMC 的非平凡示例的论文。