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

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. These results are required by a range of applications (e.g. two-dimensional turbulent transport), for which the scaling exponents are expressed via the hull’s fractal dimension.