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Dimensional dependence of phase transitions in explosive percolation.
Woosik Choi1, Huiseung Chae1, Soon-Hyung Yook1
1Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 13, 2014
Summary
This study investigates explosive percolation phase transitions across different dimensions. Results show distinct behaviors in 2D, with some models exhibiting discontinuous transitions while others show continuous ones, unlike in 3D where all models transition continuously.
Area of Science:
- Statistical Physics
- Complex Systems
- Percolation Theory
Background:
- Explosive percolation models exhibit unique phase transition behaviors.
- Understanding the influence of spatial dimensions on these transitions is crucial.
- Previous studies have introduced various models with differing enhancement or suppression mechanisms.
Purpose of the Study:
- To investigate the dependence of explosive percolation phase transition natures on space dimensions.
- To analyze the number of cutting bonds (n(cut)) and the fractal dimension of the critical spanning cluster (d(CSC)).
- To compare the behavior of six different models across 2D and 3D lattices.
Main Methods:
- Studying six distinct explosive percolation models on 2D and 3D lattices.
- Calculating the number of cutting bonds (n(cut)) and its scaling behavior.
- Determining the fractal dimension of the critical spanning cluster (d(CSC)).
- Employing finite-size scaling analyses of mean cluster size and order parameter in 3D.
Main Results:
- In 2D, intrabond-enhanced and site models show n(cut)=1 and d(CSC)≈2.00, indicating discontinuous transitions.
- In 2D, intrabond-suppressed models exhibit n(cut) scaling with d(cut)=1 and d(CSC)≈1.96, suggesting continuous transitions.
- In 3D, all six models display d(cut)>0 and d(CSC)≈2.8, consistent with continuous transitions and similar critical phenomena.
Conclusions:
- Explosive percolation models exhibit dimension-dependent phase transition behaviors.
- A clear distinction between discontinuous (2D, enhanced/site models) and continuous (2D, suppressed models) transitions is observed in two dimensions.
- All studied models undergo continuous transitions in three dimensions, with similar critical phenomena.
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