异构复杂系统中不连通簇的涌现
Emergence of disconnected clusters in heterogeneous complex systems
摘要：
逾渗理论直观地将复杂系统中的相关区域描述为紧密相连的簇。虽然这幅图可能是足够的，在小尺度上，除了临界，我们表明，高度相关的网站在复杂系统可以固有地断开。这一发现表明一个反直觉的组织动力学的相关性，其中功能相似性从物理连接。我们说明的例子的无序接触过程（DCP）的感染在异构系统中传播的现象。我们应用数值模拟和渐近精确的重整化群技术（SDRG）在1，2和3维系统，以及在二维晶格长程相互作用。我们的结论是，关键的动态是很好地捕捉大多数一个，高度相关，但空间上不连通的集群。我们的研究结果表明，在临界状态下，相关的，同时感染的网站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伊辛模型的临界行为，导致量子相关，但空间上不连通的磁畴。
英文摘要：
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.
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