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

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.

References in corpus (4)

• Inverse turbulent cascades and conformally invariant curves
• Gaussian Statistics of Fracture Surfaces
• Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution
• Contour lines of the discrete scale invariant rough surfaces

Cited by in corpus (5)

• Recent advances in percolation theory and its applications
• Recent advances and open challenges in percolation
• Percolation with long-range correlated disorder
• Retention capacity of correlated surfaces
• Efficient method of finding scaling exponents from finite-size Monte-Carlo simulations