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Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents
Y S Cho1, J S Lee2, H J Herrmann3
1CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
Physical Review Letters
|January 30, 2016
Summary
A new network growth strategy reveals a hybrid percolation transition, blending first-order and second-order properties. This finding offers insights into cluster aggregation and interdependent network dynamics.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Understanding network growth and connectivity is crucial for various fields.
- Phase transitions in complex systems often exhibit distinct first-order or second-order characteristics.
- Interdependent networks and link-deleting processes introduce unique dynamics.
Purpose of the Study:
- To investigate the phase transition behavior in a novel network growth model.
- To analyze the cluster size distribution and its implications for network structure.
- To explore the connection between this model and phenomena in interdependent networks.
Main Methods:
- Simulating a network growth process where new connections involve nodes from small clusters.
- Analyzing the cluster size distribution at the transition point.
- Comparing the observed power-law behavior with existing network models.
Main Results:
- The proposed network growth strategy induces a hybrid percolation transition.
- The cluster size distribution follows a power-law with a continuously varying exponent (2 < τ(g) ≤ 2.5).
- This transition exhibits characteristics of both first-order and second-order phase transitions.
Conclusions:
- The study identifies a novel hybrid phase transition in network aggregation.
- The findings provide a necessary condition for hybrid transitions in cluster aggregation processes.
- The observed power-law behavior offers a link to avalanche phenomena in interdependent networks.
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