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

TL;DR

This study investigates how long-range self-affine correlations influence the shape anisotropy of two-dimensional percolation clusters, revealing that self-affinity tends to make clusters more isotropic and that correlation nature affects scaling corrections.

Contribution

It introduces a numerical analysis of anisotropy in 2D percolation clusters with self-affine correlations using fractional Brownian motion, highlighting the impact of correlation type on cluster shape.

Findings

Self-affinity slightly increases isotropy of clusters.

Persistent correlations add negative correction to anisotropy.

Anti-persistent correlations add positive correction to anisotropy.

Abstract

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.