论文标题
2D刚度渗透中保形不变性的证据
Evidences of conformal invariance in 2d rigidity percolation
论文作者
论文摘要
刚性转变发生在显微镜组件的密度增加时，由于出现了跨太空刚性连接的组件或群集，无序介质能够发射并确保宏观机械稳定性。作为连续的相变，它表现出一个刻度不变的临界点，刚性簇是随机分形。我们使用数值分析表明，这些簇也是形式上不变的，我们使用保形场理论来预测通用有限大小效应的形式。此外，尽管连通性和刚性渗透通常属于不同的普遍性类别，因此从根本上具有不同的本质，但我们提供了其在关键时随机簇的统计特性之间出乎意料的相似性的证据。我们的工作通过应用功能强大的2D形成野外理论工具来开辟新的研究途径，以了解表现出这种机械过渡的广泛物理和生物材料的临界行为。
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid connected component, or cluster. As a continuous phase transition it exhibits a scale invariant critical point, at which the rigid clusters are random fractals. We show, using numerical analysis, that these clusters are also conformally invariant, and we use conformal field theory to predict the form of universal finite size effects. Furthermore, although connectivity and rigidity percolation are usually though to belong to different universality classes and thus be of fundamentally different natures, we provide evidence of unexpected similarities between the statistical properties of their random clusters at criticality. Our work opens a new research avenue through the application of the powerful 2D conformal field theory tools to understand the critical behavior of a wide range of physical and biological materials exhibiting such a mechanical transition.
