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Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network
- Source :
- Physical Review E. 89
- Publication Year :
- 2014
- Publisher :
- American Physical Society (APS), 2014.
-
Abstract
- We study bond percolation on a one-parameter family of hierarchical small-world network, and find a meta-transition between the inverted BKT transition and the abrupt transition driven by changing the network topology. It is found that the order parameter is continuous and fractal exponent is discontinuous in the inverted BKT transition, and oppositely, the former is discontinuous and the latter is continuous in the abrupt transition. The gaps of the order parameter and fractal exponent in each transition go to vanish as approaching the meta-transition point. This point corresponds to a marginal power-law transition. In the renormalization group formalism, this meta-transition corresponds to the transition between transcritical and saddle-node bifurcations of the fixed point via a pitchfork bifurcation.<br />5 pages, 5 figures
- Subjects :
- Small-world network
Statistical Mechanics (cond-mat.stat-mech)
FOS: Physical sciences
Disordered Systems and Neural Networks (cond-mat.dis-nn)
Condensed Matter - Disordered Systems and Neural Networks
Fixed point
Renormalization group
Network topology
Combinatorics
Kosterlitz–Thouless transition
Pitchfork bifurcation
Fractal
Exponent
Statistical physics
Condensed Matter - Statistical Mechanics
Mathematics
Subjects
Details
- ISSN :
- 15502376 and 15393755
- Volume :
- 89
- Database :
- OpenAIRE
- Journal :
- Physical Review E
- Accession number :
- edsair.doi.dedup.....bb35539c8c1498f7e7acd368fb28dffd