Variation of the critical percolation threshold in the Achlioptas processes

TL;DR

This paper explores various modifications of Achlioptas percolation processes, revealing how different rules affect the percolation threshold while maintaining the same universality class as classical percolation.

Contribution

It introduces new variations of Achlioptas processes, including reverse and attraction/repulsion rules, and analyzes their impact on the percolation threshold and universality class.

Findings

Different rules alter the percolation threshold values.

All models studied belong to the classical percolation universality class.

Abstract

We investigate variations of the well-known Achlioptas percolation problem, which uses the method of probing sites when building up a lattice system, or probing links when building a network, ultimately resulting in the delay of the appearance of the critical behavior. In the first variation we use two-dimensional lattices, and we apply reverse rules of the Achlioptas model, thus resulting in a speed-up rather than delay of criticality. In a second variation we apply an attractive (and repulsive) rule when building up the lattice, so that newly added sites are either attracted or repelled by the already existing clusters. All these variations result in different values of the percolation threshold, which are herewith reported. Finally, we find that all new models belong to the same universality class as classical percolation.