Crossover from standard to reduced hull for random percolation

Publisher Website
Google Scholar
Abstract
The hull (external perimeter) of percolation clusters in two dimensions is a fractal object with fractal dimension DH=74 or DH′=43 depending on how it is constructed. Here it is shown that to each hull construction there corresponds a characteristic length R* such that the fractal dimension of the hull is DH on length scales smaller than R* and DH′ on length scales larger than R*. If r0 is the elementary length used for constructing the percolation cluster and r (>r0) is the elementary length used for constructing the hull, then R* diverges as (r-r0)-a as r→r0, with a≅1.37.