Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network

Tomoaki Nogawa and Takehisa Hasegawa
Phys. Rev. E 89, 042803 – Published 7 April 2014

Abstract

We study the bond percolation on a one-parameter family of a hierarchical small-world network and find the metatransition between an inverted Berezinskii-Kosterlitz-Thouless (iBKT) transition and an abrupt transition driven by changing the network topology. It is found that the order parameter is continuous and the fractal exponent is discontinuous in the iBKT transition, and oppositely, the former is discontinuous and the latter is continuous in the abrupt transition. The gaps of the order parameter and the fractal exponent in each transition vanish as they approach the metatransition point. This point corresponds to a marginal power-law transition. In the renormalization group formalism, this metatransition corresponds to the transition between transcritical and saddle-node bifurcations of the fixed point via a pitchfork bifurcation.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 17 December 2013

DOI:https://doi.org/10.1103/PhysRevE.89.042803

©2014 American Physical Society

Authors & Affiliations

Tomoaki Nogawa*

  • Faculty of Medicine, Toho University, 5-21-16, Omori-Nishi, Ota-ku, Tokyo 143-8540, Japan

Takehisa Hasegawa

  • Graduate School of Information Science, Tohoku University, 6-3-09, Aramaki-Aza-Aoba, Sendai, Miyagi 980-8579, Japan

  • *nogawa@med.toho-u.ac.jp
  • hasegawa@m.tohoku.ac.jp

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 89, Iss. 4 — April 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×