Publication

Renormalization Group for Critical Phenomena in Complex Networks

Downloadable Content

Persistent URL
Last modified
  • 02/20/2025
Type of Material
Authors
    Stefan Boettcher, Emory UniversityC.T. Brunson, Emory University
Language
  • English
Date
  • 2011-12-19
Publisher
  • Frontiers
Publication Version
Copyright Statement
  • © 2011 Boettcher and Brunson.
License
Final Published Version (URL)
Title of Journal or Parent Work
ISSN
  • 1664-042X
Volume
  • 2
Issue
  • 102
Start Page
  • 1
End Page
  • 8
Abstract
  • We discuss the behavior of statistical models on a novel class of complex “Hanoi” networks. Such modeling is often the cornerstone for the understanding of many dynamical processes in complex networks. Hanoi networks are special because they integrate small-world hierarchies common to many social and economical structures with the inevitable geometry of the real world these structures exist in. In addition, their design allows exact results to be obtained with the venerable renormalization group (RG). Our treatment will provide a detailed, pedagogical introduction to RG. In particular, we will study the Ising model with RG, for which the fixed points are determined and the RG flow is analyzed. We show that the small-world bonds result in non-universal behavior. It is shown that a diversity of different behaviors can be observed with seemingly small changes in the structure of hierarchical networks generally, and we provide a general theory to describe our findings.
Author Notes
  • Correspondence: S. Boettcher, Department of Physics, Emory University, Atlanta, GA 30322, USA. e-mail: sboettc@emory.edu
Keywords
Research Categories
  • Physics, General
  • Biology, Physiology

Tools

Relations

In Collection:

Items

Thumbnail Title File Description Date Uploaded Visibility Actions
file details Publication File - twxrf.pdf Primary Content 2025-02-03 Public Download