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Explosive percolation is continuous, but with unusual finite size behavior
Peter Grassberger1, Claire Christensen, Golnoosh Bizhani
1FZ Jülich, Jülich, Germany.
Physical Review Letters
|June 28, 2011
Summary
This study investigates explosive percolation transitions in Achlioptas-type processes. Despite continuous transitions, unique scaling behaviors and distinct universality classes were observed for the order parameter distribution.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Percolation transitions are critical phenomena in disordered systems.
- Achlioptas-type processes exhibit unique 'explosive' percolation behaviors.
Purpose of the Study:
- To analyze the characteristics of explosive percolation transitions in four Achlioptas-type models.
- To determine the universality classes and scaling properties of these processes.
Main Methods:
- Investigated finite size scaling functions.
- Analyzed the distribution of the largest cluster size (order parameter).
- Calculated critical exponents β and Θ.
Main Results:
- Observed continuous, yet non-holomorphic, finite size scaling.
- Found double-humped order parameter distributions with peaks approaching with system size N.
- Determined distinct positive values for exponent β, indicating different universality classes.
- Found exponent Θ consistently near 1/2 across all models.
Conclusions:
- The studied Achlioptas-type processes represent distinct universality classes.
- The exponent Θ ≈ 1/2 suggests a universal scaling behavior for these models.
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