Phase transition without global ordering in a hierarchical scale-free network

Takehisa Hasegawa, Masataka Sato, Koji Nemoto

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites. Surprisingly, when each site is unoccupied even with a small probability, the system permits neither the percolating phase nor the nonpercolating phase, but rather only critical phases. Although the order parameter always remains zero, a transition still exists between the critical phases that is characterized by the value of the fractal exponent, which measures the degree of criticality; the system changes from one critical state to another with the jump of the fractal exponent at the transition point. The phase boundary depends on the fraction of occupied sites. When the fraction of unoccupied sites exceeds a certain value, the transition line between the critical phases disappears, and a unique critical phase remains.

Original languageEnglish
Article number017101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume85
Issue number1
DOIs
Publication statusPublished - 2012 Jan 9

ASJC Scopus subject areas

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

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