Agglomerative percolation in two dimensions
Complexity Science Group, University of Calgary - Calgary T2N 1N4, Canada
2 FZ Jülich - D-52425 Jülich, Germany, EU
Accepted: 18 November 2011
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 —violating blatantly the basic notion of universality.
PACS: 64.60.ah – Percolation / 68.43.Jk – Diffusion of adsorbates, kinetics of coarsening and aggregation / 89.75.Da – Systems obeying scaling laws
© EPLA, 2012