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

TL;DR

This paper demonstrates that explosive percolation in an event-based ensemble follows standard finite-size scaling, clarifying previous anomalous observations and enabling precise determination of critical points and exponents across dimensions.

Contribution

The study shows that explosive percolation obeys standard scaling laws in an event-based ensemble, resolving prior anomalies and enabling accurate critical parameter estimation.

Findings

Critical behaviors follow standard finite-size scaling.

Multiple fractal structures emerge within fluctuation windows.

Critical points and exponents are precisely determined for various rules.

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.