Renormalization Group for Critical Phenomena in Complex Networks

Frontiers in Physiology

Stefan eBoettcher¹ 

[1] Emory University;

关键词: Ising Model;    complex networks;    Critical Phenomena;    Hanoi networks;    Renormalization Group;   

DOI  :  10.3389/fphys.2011.00102

来源: DOAJ

【 摘 要 】

We discuss the behavior ofstatistical models on a novel classof complex ``Hanoi'' networks. Such modeling is often the cornerstonefor the understanding of many dynamical processes in complexnetworks. Hanoi networks are special because they integratesmall-world hierarchies common to many social and economicalstructures with the inevitable geometry of the real work thesestructures exist in. In addition, their design allows emph{exact}results to be obtained with the venerable renormalization group(RG). Our treatment will provide a detailed, pedagogical introductionto RG. In particular, we will study the Ising model with RG, for whichthe fixed-points are determined and the RG-flow is analyzed.We showthat the small-world bonds result in non-universal behavior. It isshown that a diversity of different behaviors can be observed withseemingly small changes in the structure of hierarchical networksgenerally, and we provide a general theory to describe our findings.

【 授权许可】

Unknown