Fast realization of a spatially correlated percolation model

TL;DR

This paper introduces two efficient schemes for simulating spatially correlated percolation models and combines them with a generalized Newman-Ziff algorithm to analyze percolation thresholds in correlated systems.

Contribution

The paper presents novel schemes for fast realization of correlated percolation models and extends the Newman-Ziff algorithm to include correlations.

Findings

Correlations influence percolation thresholds in a limited phase space.

The proposed schemes are efficient in different correlation regimes.

Spatial correlations have a minor effect on the overall phase space.

Abstract

We propose two schemes to achieve fast realizations of spatially correlated percolation models. The schemes are shown to be efficient in complementary regimes of correlation phase space. They are combined with a generalized Newman-Ziff algorithm to numerically determine the percolation thresholds of two-dimensional lattices in the presence of correlations. It is found that the spatial correlations affect only a relatively small part of phase space.