Monte-Carlo study of scaling exponents of rough surfaces and correlated percolation

TL;DR

This study uses Monte Carlo simulations to determine how the scaling exponents of two-dimensional correlated percolation clusters depend on the Hurst exponent, confirming previous conjectures about their behavior.

Contribution

It provides the first comprehensive numerical analysis of the scaling exponents of correlated percolation clusters as functions of the Hurst exponent.

Findings

Scaling exponents vary with Hurst exponent H.

Results confirm earlier theoretical conjectures.

Provides detailed numerical data for H in [-0.75, 1].

Abstract

We calculate the scaling exponents of the two-dimensional correlated percolation cluster's hull and unscreened perimeter. Correlations are introduced through an underlying correlated random potential, which is used to define the state of bonds of a two-dimensional bond percolation model. Monte-Carlo simulations are run and the values of the scaling exponents are determined as functions of the Hurst exponent H in the range -0.75 <= H <= 1. The results confirm the conjectures of earlier studies.