Agglomerative Percolation in Two Dimensions
Statistical Mechanics
2015-03-17 v4
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.
Cite
@article{arxiv.1012.1070,
title = {Agglomerative Percolation in Two Dimensions},
author = {Claire Christensen and Golnoosh Bizhani and Seung-Woo Son and Maya Paczuski and Peter Grassberger},
journal= {arXiv preprint arXiv:1012.1070},
year = {2015}
}
Comments
Paper and supplementary figures and discussion