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Continuous percolation phase transitions of random networks under a generalized Achlioptas process
Jingfang Fan1, Maoxin Liu, Liangsheng Li
1State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
Researchers studied evolving random networks using a generalized Achlioptas process (GAP). They found continuous phase transitions, with critical exponents and universality classes depending on the probability parameter p.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Percolation theory studies connectivity in random graphs.
- Achlioptas processes introduce novel mechanisms for network evolution.
- Understanding phase transitions in evolving networks is crucial for various applications.
Purpose of the Study:
- Investigate percolation phase transitions in evolving random networks under a generalized Achlioptas process (GAP).
- Analyze the impact of the probability parameter 'p' on network properties and universality classes.
- Determine critical exponents governing the phase transitions.
Main Methods:
- Employed finite-size scaling techniques.
- Utilized the generalized Achlioptas process (GAP) with varying probability 'p'.
- Analyzed the fixed point of the size ratio s{2}/s{1} and the behavior of lns{1} at the critical point.
Main Results:
- Demonstrated continuous phase transitions for 0.5 ≤ p ≤ 1.
- Identified critical exponents β and ν from the slopes of lns{1} and ln(s{2}/s{1})'.
- Observed a stable universality class for 0.5 ≤ p ≤ 0.8, and a p-dependent universality class for p ≥ 0.9.
Conclusions:
- The generalized Achlioptas process exhibits continuous phase transitions.
- The universality class of these transitions is consistent across a range of 'p' but becomes dependent on 'p' at higher values.
- This research provides insights into the fundamental behavior of evolving complex networks.
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