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arXiv · 1012.1070

Agglomerative Percolation in Two Dimensions

Claire Christensen·Golnoosh Bizhani·Seung-Woo Son·Maya Paczuski·Peter Grassberger
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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.

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Claire Christensen, Golnoosh Bizhani, Seung-Woo Son, Maya Paczuski, Peter Grassberger. 2010-12-06. Agglomerative Percolation in Two Dimensions. https://arxiv.org/abs/1012.1070

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