Enclosed area distribution in percolation
arXiv:cond-mat/0510633
Abstract
The number of two-dimensional percolation clusters whose external hulls enclose an area greater than A, in a system of area Omega, behaves at the critical point as C Ω/A for large A, where C = 1/(8 pi sqrt(3)). Here we show that away from the critical point this factor is multiplied by a scaling function that is asymptotically proportional to a simple exponential exp(-A/A*) where A* scales as |p - pc|^(-2 nu). The fit is better than for Kunz and Souillard sub-critical scaling, which would predict the asymptotic behavior exp(-(A/A*)^(2/D) where D = 91/48 is the fractal dimension.
Talk presented in the StatPhys22 conference in Bangalore, India, July 5-9 2004