Explosive Percolation Obeys Standard Finite-Size Scaling in an Event-based Ensemble

Abstract

Explosive percolation in the Achlioptas process, which has attracted much research attention, is known to exhibit a rich variety of critical phenomena that are anomalous from the perspective of continuous phase transitions. Hereby, we show that, in an event-based ensemble, the critical behaviors in explosive percolation are rather clean and obey the standard finite-size scaling theory, except for the large fluctuation of pseudo-critical points. In the fluctuation window, multiple fractal structures emerge and the values can be derived from a crossover scaling theory. Further, their mixing effects account well for the previously observed anomalous phenomena. Making use of the clean scaling in the event-based ensemble, we determine with a high precision the critical points and exponents for a number of bond-insertion rules, and clarify ambiguities about their universalities. Our findings hold true for any spatial dimensions.

5 pages, 4 figures

References in corpus (6)

• Recent advances in percolation theory and its applications
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Explosive percolation in scale-free networks
• Universality class of epidemic percolation transitions driven by random walks

Cited by in corpus (13)

• Shortest-path percolation on random networks
• Explosive percolation in finite dimensions
• Emergence of biconnected clusters in explosive percolation
• Universality of random-site percolation thresholds for two-dimensional complex non-compact neighborhoods
• Link rewiring with local information--induced hybrid percolation transitions
• Finite-size scaling of percolation on scale-free networks
• Explosive percolation on the Bethe lattice is ordinary
• Universality of percolation at dynamic pseudocritical point
• Discontinuous percolation via suppression of neighboring clusters in a network
• Thermodynamic analysis of diverse percolation transitions
• Locality approach to the bootstrap percolation paradox
• Shortest-path percolation on scale-free networks
• Anomalous criticality coexists with giant cluster in the uniform forest model