Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks

TL;DR

This paper investigates a biased dynamic percolation process on 2D lattices, revealing an explosive, first-order phase transition with unique critical behavior distinct from standard percolation.

Contribution

It introduces a cooperative Achlioptas-type process with cluster-dependent bond selection, demonstrating a new universality class for the phase transition.

Findings

Exhibits an explosive, first-order phase transition in cluster growth.

Shows a sharp jump in the largest cluster size at criticality.

Identifies a different universality class from standard percolation.

Abstract

The growth of two-dimensional lattice bond percolation clusters through a cooperative Achlioptas-type of process, where the choice of which bond to occupy next depends upon the masses of the clusters it connects, is shown to go through an explosive, first-order kinetic phase transition with a sharp jump in the mass of the largest cluster as the number of bonds is increased. The critical behavior of this growth model is shown to be of a different universality class than standard percolation.