Solution of the explosive percolation quest: Scaling functions and critical exponents

TL;DR

This paper develops a comprehensive scaling theory for explosive percolation, revealing that its phase transition is continuous with very small critical exponents, and provides detailed scaling functions and critical parameters.

Contribution

It introduces a strict scaling framework for explosive percolation, clarifying its continuous transition and characterizing its critical exponents and scaling functions.

Findings

Transition is continuous despite initial beliefs of discontinuity.

Provides explicit scaling functions and critical exponents.

Explains the exotic properties of the transition.

Abstract

Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently when in a new so-called "explosive percolation" problem for a competition driven process, a discontinuous phase transition was reported. The analysis of evolution equations for this process showed however that this transition is actually continuous though with surprisingly tiny critical exponents. For a wide class of representative models, we develop a strict scaling theory of this exotic transition which provides the full set of scaling functions and critical exponents. This theory indicates the relevant order parameter and susceptibility for the problem, and explains the continuous nature of this transition and its unusual properties.