Explosive site percolation with a product rule

Abstract

We study the site percolation under Achlioptas process (AP) with a product rule in a $2-dimensional$ (2D) square lattice. From the measurement of the cluster size distribution, $P_s$, we find that $P_s$ has a very robust power-law regime followed by a stable hump near the transition threshold. Based on the careful analysis on the $P_s$ distribution, we show that the transition should be discontinuous. The existence of the hysteresis loop in order parameter also verifies that the transition is discontinuous in 2D. Moreover we also show that the transition nature from the product rule is not the same as that from a sum rule in 2D.

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• Explosive Percolation: Unusual Transitions of a Simple Model
• Unstable supercritical discontinuous percolation transitions
• Explosive percolations on the Bethe Lattice
• Critical exponents of the explosive percolation transition
• Critical behaviors and universality classes of percolation phase transitions on two-dimensional square lattice
• Criticality and Continuity of Explosive Site Percolation in Random Networks
• Product-Sum universality and Rushbrooke inequality in explosive percolation
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• Hysteresis and criticality in hybrid percolation transitions
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• Universality class of explosive percolation in Barabási-Albert networks
• Explosive percolation on the Bethe lattice is ordinary
• Discontinuous transition in explosive percolation via local suppression
• Discontinuous percolation via suppression of neighboring clusters in a network
• Discontinuous emergence of a giant cluster in assortative scale-free networks