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Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network

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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

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