Percolation with long-range correlated disorder

TL;DR

This study uses Monte Carlo simulations to explore how long-range spatial correlations affect percolation properties, revealing how critical exponents depend on the Hurst exponent and analyzing structural and transport characteristics.

Contribution

It provides new insights into the critical behavior of correlated percolation, including functional dependencies of exponents on the Hurst parameter and detailed structural analysis.

Findings

Critical exponents vary with Hurst exponent H

Fractal dimension of the largest cluster depends on H

Transport properties are influenced by spatial correlations

Abstract

Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as function of the Hurst exponent $H$ which characterizes the degree of spatial correlation among the occupation of sites. In particular, we study the fractal dimension of the largest cluster and the scaling behavior of the second moment of the cluster size distribution, as well as the complete and accessible perimeters of the largest cluster. Concerning the inner structure and transport properties of the largest cluster, we analyze its shortest path, backbone, red sites, and conductivity. Finally, bridge site growth is also considered. We propose expressions for the functional dependence of the critical exponents on $H$.