Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network
Title: | Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network |
Authors: | Nogawa, Tomoaki Browse this author | Hasegawa, Takehisa Browse this author | Nemoto, Koji Browse this author →KAKEN DB |
Issue Date: | Sep-2012 |
Publisher: | American Physical Society |
Journal Title: | Physical Review E |
Volume: | 86 |
Issue: | 3 |
Start Page: | 030102 |
Publisher DOI: | 10.1103/PhysRevE.86.030102 |
Abstract: | We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point. |
Rights: | ©2012 American Physical Society |
Type: | article |
URI: | http://hdl.handle.net/2115/50284 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 根本 幸児
|