The anisotropy of two dimensional percolation clusters of self-affine models

The anisotropy parameter of two-dimensional equilibrium clusters of site percolation process in long-range self-affine correlated structures are studied numerically. We use a fractional Brownian Motion(FBM) statistic to produce both persistent and anti-persistent long-range correlations in 2-D models. It is seen that self affinity makes the shape of percolation clusters slightly more isotropic. Moreover, we find that the sign of correction to scaling term is determined by the nature of correlation. For persistent correlation the correction to scaling term adds a negative contribution to the anisotropy of percolation clusters, while for the anti-persistent case it is positive.