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Finite-size scaling theory for explosive percolation transitions
1Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
We developed a new finite-size scaling theory for explosive percolation transitions, which are discontinuous. This new approach successfully describes critical behavior and susceptibility using numerical data.
Area of Science:
- Statistical Physics
- Complex Networks
- Phase Transitions
Background:
- Finite-size scaling (FSS) theory is established for continuous phase transitions.
- FSS is not well-established for discontinuous phase transitions like explosive percolation.
- Explosive percolation transitions occur in models like Erdős and Rényi with the Achlioptas process.
Purpose of the Study:
- To develop a finite-size scaling (FSS) theory for explosive percolation transitions.
- To establish a method for analyzing critical behavior in discontinuous phase transitions.
Main Methods:
- Derived a novel scaling function based on the power-law divergence of the order parameter's derivative at the critical point.
- Applied this scaling function to analyze the susceptibility.
- Used numerical simulation data for various system sizes.
Main Results:
- The new FSS theory successfully describes the explosive percolation transition.
- The derived scaling function accurately collapses numerical data for different system sizes.
- Susceptibility also follows the established scaling form.
Conclusions:
- The developed FSS theory provides a robust framework for studying discontinuous phase transitions.
- This work extends the applicability of FSS to a broader range of critical phenomena.
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