Explosive percolation on a scale-free multifractal weighted planar stochastic lattice

Area of Science:

• Statistical Physics
• Network Science
• Complex Systems

Background:

• Explosive percolation (EP) exhibits a delayed onset of spanning clusters compared to random bond percolation (RBP).
• The order of the EP transition and its critical exponents remain largely uncharacterized, unlike classical random percolation.

Purpose of the Study:

• Investigate explosive bond percolation (EBP) using the Achlioptas process on a scale-free multifractal weighted planar stochastic lattice.
• Determine the critical point, critical exponents (β, γ, ν), Fisher exponent (τ), and fractal dimension (d_f) for EBP.
• Compare EBP characteristics with RBP to understand universality classes and scaling relations.

Main Methods:

• Numerical determination of the critical point (p_c).
• Calculation of critical exponents (β, γ, ν), Fisher exponent (τ), and fractal dimension (d_f).
• Comparative analysis of scaling relations between EBP and RBP.

Main Results:

• The critical point p_c was numerically found.
• All critical exponents and fractal dimensions for EBP were obtained.
• EBP exponents were found to obey the same scaling relations as RBP.
• A significantly smaller value for the critical exponent β in EBP compared to RBP was observed.

Conclusions:

• Explosive bond percolation (EBP) on this complex lattice shares scaling relations with random bond percolation (RBP).
• The unusually small critical exponent β distinguishes EBP, suggesting it is not entirely special beyond this exponent.
• Further research is needed to fully classify EBP within universality classes.