A picture of thermal QCD phase change based on the analogy with metal-to-insulator transition of Anderson type was proposed in the past. In this picture, a low-T thermal state is akin to a metal with deeply infrared (IR) Dirac modes abundant and extended, while a high-T state is akin to an insulator with IR modes depleted and localized below a mobility edge ${\lambda }_{\mathrm{\text{A}}}>0$. Here we argue that, while ${\lambda }_{\mathrm{\text{A}}}$ exists in QCD, a high-T state is not an insulator in such an analogy. Rather, it is a critical state arising due to a new singular mobility edge at ${\lambda }_{\mathrm{\text{IR}}}=0$. This new mobility edge appears upon the transition into the recently proposed IR phase. As a key part of such a metal-to-critical scenario, we present evidence using pure-glue QCD that deeply infrared Dirac modes in the IR phase extend to arbitrarily long distances. This is consistent with our previous suggestion that the IR phase supports scale invariance in the infrared. We discuss the role of Anderson-like aspects in this thermal regime and emphasize that the combination of gauge field topology and disorder plays a key role in shaping its IR physics. Our conclusions are conveyed by the structure of Dirac spectral non-analyticities.

基于与安德森型金属到绝缘体转变的类比，过去提出了热QCD相变图。在这张图片中，低T热态类似于具有丰富和扩展的深红外 (IR) 狄拉克模式的金属，而高T态类似于具有耗尽的 IR 模式并位于迁移率边缘以下的绝缘体${\lambda }_{\mathrm{\text{一个}}}>0$. 在这里我们认为，虽然${\lambda }_{\mathrm{\text{一个}}}$在 QCD 中存在，高T状态在这样的类比中不是绝缘体。相反，它是由于新的奇异流动性边缘而出现的临界状态${\lambda }_{\mathrm{\text{红外}}}=0$. 这种新的移动性优势出现在过渡到最近提出的 IR 阶段时。作为这种金属到临界情景的关键部分，我们使用纯胶 QCD 提供证据，证明 IR 阶段的深红外狄拉克模式可以延伸到任意长距离。这与我们之前的建议一致，即 IR 相位支持红外中的尺度不变性。我们讨论了类安德森方面在这种热状态中的作用，并强调规范场拓扑和无序的组合在塑造其红外物理方面起着关键作用。我们的结论是由狄拉克谱非解析的结构传达的。