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Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks
1Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA. rziff@umich.edu
Physical Review Letters
|August 8, 2009
Summary
This study reveals explosive phase transitions in lattice bond percolation growth. The largest cluster
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Percolation theory models random processes on lattices.
- Standard percolation lacks cooperative growth mechanisms.
Purpose of the Study:
- Investigate cooperative growth in 2D lattice bond percolation.
- Analyze phase transitions in Achlioptas-type processes.
Main Methods:
- Simulated cooperative Achlioptas-type bond occupation.
- Analyzed cluster mass growth dynamics.
- Examined critical behavior and universality classes.
Main Results:
- Observed an explosive, first-order kinetic phase transition.
- Demonstrated a sharp jump in the largest cluster's mass.
- Identified a distinct universality class compared to standard percolation.
Conclusions:
- Cooperative growth leads to abrupt phase transitions.
- This model exhibits unique critical phenomena.
- Challenges traditional percolation universality assumptions.
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