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Critical behavior of k-core percolation: Numerical studies
Deokjae Lee1, Minjae Jo1, B Kahng1
1Department of Physics and Astronomy, CCSS, CTP, Seoul National University, Seoul 08826, Korea.
Physical Review. E
|January 14, 2017
Summary
K-core percolation, a model for discontinuous transitions, exhibits a hybrid phase transition with critical behavior. This study reveals distinct critical exponents for order parameters and avalanche sizes in Erdős-Rényi networks.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- K-core percolation is a long-standing model for discontinuous percolation.
- Recent findings indicate critical behavior in the order parameter of k-core percolation on random networks, suggesting a hybrid phase transition.
- The critical behaviors of these hybrid transitions are not yet fully understood.
Purpose of the Study:
- To investigate the critical behavior of k-core percolation specifically in Erdős-Rényi networks.
- To elucidate the nature of the hybrid phase transition in this context.
- To understand the relationship between order parameter critical behavior and finite avalanche dynamics.
Main Methods:
- Numerical investigation of k-core percolation on Erdős-Rényi random networks.
- Analysis of the fluctuations of the order parameter.
- Calculation and analysis of the mean avalanche size.
Main Results:
- Numerical evidence shows that the order parameter fluctuations and mean avalanche size diverge differently.
- Critical exponents are classified into two types: those related to the order parameter and those related to finite avalanches.
- While conventional scaling relations hold within each set, the two sets of critical exponents are coupled.
Conclusions:
- K-core percolation on Erdős-Rényi networks exhibits a hybrid phase transition with distinct critical behaviors.
- The study provides a new classification of critical exponents for hybrid transitions.
- Universal features of k-core percolation and cascade failures on multiplex networks are discussed.
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