Loop structure of percolation hulls.

Abstract

The loop structure generated by the percolation hulls in two dimensions is investigated both for random percolation and for the percolation properties of interacting, diffusing particles using the gradient diffusion method. Scaling forms for the loop distribution function are proposed and verified numerically. The results show that while bonding nearby particles on the original hull reduces its fractal dimension from ${\mathrm{D}}_{\mathrm{H}}$=74 to ${\mathrm{D}}_{\mathrm{H}\ensuremath{'}}$=43, no further change in ${\mathrm{D}}_{\mathrm{H}\ensuremath{'}}$ is observed when additional bonds are placed on the already reduced hull. A similar behavior holds for strongly interacting particles during phase separation on length scales larger than the characteristic droplet size.