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

Tomoaki Nogawa, Takehisa Hasegawa, Koji Nemoto

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Article number030102
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number3
DOIs
Publication statusPublished - 2012 Sep 11

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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