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Published on: February 25, 2015
Critical phenomena in heterogeneous k-core percolation.
Davide Cellai1, Aonghus Lawlor, Kenneth A Dawson
1MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
Summary
Heterogeneous k-core percolation models network resilience with varied vertex durability. Binary mixtures reveal critical and tricritical points, with exponents linking to glass transition models.
Area of Science:
- Network Science
- Statistical Physics
Background:
- K-core percolation models network functionality and resilience.
- Analyzing network resilience under damage is crucial.
Purpose of the Study:
- Introduce and investigate heterogeneous k-core percolation.
- Analyze binary mixtures in configuration model networks.
- Categorize critical phenomena and identify tricritical points.
Main Methods:
- Analytical investigation of binary mixtures.
- Study within a wide class of configuration model networks.
- Calculation of critical exponents.
Main Results:
- Observed critical and tricritical points.
- Provided a general criterion for tricritical point occurrence.
- Identified universality classes shared with facilitated spin models.
Conclusions:
- Heterogeneous k-core percolation exhibits rich critical phenomena.
- The model's behavior can be linked to glass transition physics.
- Analytical methods provide insights into network resilience.
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