Numerical simulations of the phase transition property of the explosive percolation model on Erds Rnyi random network

Abstract

Based on the modified Newman and Ziff algorithm combined with the finite-size scaling theory, in this present work we analytically study the phase transition property of the explosive percolation model induced by Achlioptas process on the Erds Rnyi random network via numerical simulations for the basic percolation quantities including the order parameter, the average cluster size, the moments, the standard deviation and the cluster heterogeneity. It is explicitly shown that all these relevant quantities display a typical power-law scaling behavior, which is the characteristic of continuous phase transition at the percolation threshold despite the fact that the order parameter presents a certain feature of discontinuous transition at the same time. Strictly, the explosive percolation transition during the Erds Rnyi random network is a singular transition, which means that it is neither a standard discontinuous phase transition nor the continuous transition in the regular random percolation model.