"Explosive Percolation" Transition is Actually Continuous

TL;DR

This paper demonstrates through analytical and numerical methods that the so-called explosive percolation transition, previously thought to be discontinuous, is actually a continuous phase transition with a very small critical exponent.

Contribution

The authors provide rigorous analytical and numerical evidence that explosive percolation transitions are continuous, challenging prior claims of discontinuity.

Findings

Explosive percolation transition is continuous.

The transition has a very small critical exponent.

Provides a new class of critical phenomena in irreversible systems.

Abstract

The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase transitions were believed to be continuous, however, in 2009, a remarkably different, discontinuous phase transition was reported in a new so-called "explosive percolation" problem. Each link in this problem is established by a specific optimization process. Here, employing strict analytical arguments and numerical calculations, we find that in fact the "explosive percolation" transition is continuous though with an uniquely small critical exponent of the percolation cluster size. These transitions provide a new class of critical phenomena in irreversible systems and processes.