Explosive percolation via control of the largest cluster

TL;DR

This paper demonstrates that focusing solely on the largest cluster can induce a first-order percolation transition with Gaussian cluster distributions and fractal perimeters, advancing understanding of explosive percolation phenomena.

Contribution

It introduces a model where controlling only the largest cluster results in a first-order transition with Gaussian and compact clusters, differing from previous models.

Findings

First-order transition achieved by controlling the largest cluster.

Clusters are Gaussian and compact at the transition.

Perimeters of clusters are fractal with a dimension of approximately 1.23.

Abstract

We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the transition point, yielding a fractal dimension of $1.23\pm0.03$, close to that of watersheds.