The Nature of Explosive Percolation Phase Transition

Abstract

In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and square lattice. In finite system, two well-defined Gaussian-like peaks coexist, and the valley between the two peaks is suppressed with the system size increasing. This finite-size effect always appears in typical first-order phase transition. However, both of the two peaks shift to zero point in a power law manner, which indicates the explosive percolation is continuous in the thermodynamic limit. The nature of explosive percolation in all the three structures belongs to this novel continuous phase transition. Various scaling exponents concerning the order-parameter-distribution are obtained.