Agglomerative Percolation in Two Dimensions

TL;DR

This paper investigates a novel agglomerative percolation process in two dimensions, revealing different critical behaviors depending on lattice type and cluster selection rules, including a new universality class.

Contribution

It introduces and analyzes agglomerative percolation in 2D, demonstrating new critical phenomena and universality classes distinct from ordinary percolation.

Findings

Continuous transition on square lattice with equal cluster selection

Runaway compact cluster with mass-proportional targeting

Same critical exponents as ordinary percolation on triangular lattice

Abstract

We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging length scale near a critical point. Picking target clusters with probability proportional to their mass leads to a runaway compact cluster. Choosing all clusters equally leads to a continuous transition in a new universality class for the square lattice, while the transition on the triangular lattice has the same critical exponents as ordinary percolation.