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Critical exponents of the explosive percolation transition
R A da Costa1, S N Dorogovtsev2, A V Goltsev2
1Departamento de Física da Universidade de Aveiro & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.
Summary
Researchers clarified that "explosive percolation transition" is a continuous, second-order phase transition, not discontinuous. They developed a numerical method to accurately determine critical exponents and characteristics for these complex network models.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- Percolation theory studies how connected components form in random networks.
- Nonequilibrium models with preferential attachment, termed 'explosive percolation,' were initially thought to exhibit discontinuous phase transitions.
- Previous simulations suggested a sudden, discontinuous emergence of the percolation cluster.
Purpose of the Study:
- To re-evaluate the nature of the explosive percolation transition.
- To develop an efficient numerical method for analyzing second-order phase transitions in explosive percolation models.
- To accurately determine critical exponents and other characteristics for various explosive percolation models.
Main Methods:
- Proposed an efficient numerical method combining solutions of evolution equations for cluster size distribution.
- Incorporated power-law asymptotics to analyze the transition behavior.
- Applied the method to representative explosive percolation models with varying numbers of connection choices.
Main Results:
- Demonstrated that the explosive percolation transition is continuous (second order), contrary to prior conclusions.
- Observed anomalously small critical exponents for the percolation cluster in this continuous transition.
- Achieved high precision in determining critical exponents and critical points for multiple models.
Conclusions:
- The explosive percolation transition is a continuous, second-order phenomenon.
- The developed numerical method accurately characterizes these transitions and their critical properties.
- Findings provide a refined understanding of phase transitions in complex nonequilibrium network models.
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