The Nature of Explosive Percolation Phase Transition

TL;DR

This paper demonstrates that explosive percolation, previously thought to be discontinuous, is actually a continuous phase transition in the thermodynamic limit, supported by analysis of order-parameter distributions across different network types.

Contribution

It reveals that explosive percolation is a continuous phase transition, challenging prior assumptions and providing detailed scaling analysis across various network structures.

Findings

Order-parameter-distribution peaks shift to zero as system size increases

Finite-size effects resemble first-order transitions but are actually continuous

Scaling exponents for the distribution are obtained

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.