Explosive percolation in graphs

TL;DR

This paper investigates explosive percolation, a process with competitive link addition that was thought to cause abrupt phase transitions, and finds that the transition is actually continuous across various graph types.

Contribution

It provides a comprehensive numerical survey of explosive percolation on different graphs, confirming recent analytical results that the transition is continuous.

Findings

Explosive percolation transition is continuous, not discontinuous.

Results are consistent across lattices and scale-free networks.

Numerical evidence supports recent analytical work.

Abstract

Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the same probability. However, alternative rules for the occupation of sites/bonds might affect the order of the transition. A recent set of rules proposed by Achlioptas et al. [Science 323, 1453 (2009)], characterized by competitive link addition, was claimed to lead to a discontinuous connectedness transition, named "explosive percolation". In this work we survey a numerical study of the explosive percolation transition on various types of graphs, from lattices to scale-free networks, and show the consistency of these results with recent analytical work showing that the transition is actually continuous.