Agglomerative Percolation in Two Dimensions

Details Agglomerative Percolation in Two Dimensions Agglomerative Percolation in Two Dimensions

2010-12-06

arxiv.org/abs/1012.1070v4

Physics

Condensed Matter

Statistical Mechanics

Paper and supplementary figures and discussion

Scientific paper

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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