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

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.

Automated summary

Explosive percolation in the Achlioptas process exhibits a variety of anomalous critical phenomena, which are different from continuous phase transitions. In an event-based ensemble, we find that the critical behaviors in explosive percolation are clean and follow standard finite-size scaling theory, except for fluctuations in pseudo-critical points. Multiple fractal structures emerge in the fluctuation window and their values can be derived from a crossover scaling theory. The mixing effects of these structures explain the previously observed anomalous phenomena. The clean scaling in the event-based ensemble allows us to determine the critical points and exponents for various bond-insertion rules with high precision, resolving ambiguities about their universality. The findings hold true for any spatial dimensions.