Fractal dimension and threshold properties in a spatially correlated percolation model

TL;DR

This paper investigates how spatial correlations affect percolation thresholds and fractal dimensions in a 2D site percolation model, revealing that correlations significantly alter cluster fractal properties but not the percolation threshold.

Contribution

It introduces a generalized Monte Carlo algorithm to study spatial correlations in percolation and analyzes their impact on critical properties.

Findings

Percolation thresholds remain close to uncorrelated values across correlations.

Fractal dimensions of clusters are significantly affected by correlations.

Long-range correlations influence cluster geometry more than percolation threshold.

Abstract

We consider the effects of spatial correlations in a two-dimensional site percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to include spatial correlations, percolation thresholds and fractal dimensions of percolation clusters are obtained. For a wide range of spatial correlations, the percolation threshold differs little from the uncorrelated result. In contrast, the fractal dimension differs sharply from the uncorrelated result for almost all types of correlation studied. We interpret these results in the framework of long-range correlated percolation.