Fractal dimension and threshold properties in a spatially correlated percolation model

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.

Alternative criterion for two-dimensional wrapping percolation

“…In comparison with Machta's method, although our method is not competitive in computation time, it provides a unified method for wrapping percolation and spanning percolation. This work helps us to choose an appropriate method for the further study of some kind of spatially correlated percolation model [28], where the percolation thresholds have not yet been well determined.…”