论文标题
异质复合系统中断开簇的出现
Emergence of disconnected clusters in heterogeneous complex systems
论文作者
论文摘要
渗透理论决定了一个直观的图像，该图片将复杂系统中相关区域描述为密度连接的簇。尽管此图片在小规模上可能足够，除了临界之外，我们表明复杂系统中高度相关的位点可以固有地断开连接。这一发现表明了动态相关性的反直觉组织，其中功能相似性将其与物理连通性解脱。我们以异质系统中感染的无序接触过程（DCP）为例说明了现象。我们在1、2和3尺寸系统以及具有长期相互作用的二维晶格中应用数值模拟和渐近重新归一化组技术（SDRG）。我们得出的结论是，临界动力学大多是一个高度相关但在空间断开的集群中很好地捕获的。我们的发现表明，相关的，同时感染的位点通常不会直接相互作用。由于SDRG方程的相似性，我们的结果也适用于无序量子ISING模型的临界行为，从而导致量子相关，但在空间上断开了磁性域。
Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated sites in complex systems can be inherently disconnected. This finding indicates a counter-intuitive organization of dynamical correlations, where functional similarity decouples from physical connectivity. We illustrate the phenomena on the example of the Disordered Contact Process (DCP) of infection spreading in heterogeneous systems. We apply numerical simulations and an asymptotically exact renormalization group technique (SDRG) in 1, 2 and 3 dimensional systems as well as in two-dimensional lattices with long-ranged interactions. We conclude that the critical dynamics is well captured by mostly one, highly correlated, but spatially disconnected cluster. Our findings indicate that at criticality the relevant, simultaneously infected sites typically do not directly interact with each other. Due to the similarity of the SDRG equations, our results hold also for the critical behavior of the disordered quantum Ising model, leading to quantum correlated, yet spatially disconnected, magnetic domains.
