# Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects.

@article{Zierenberg2017PercolationTA, title={Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects.}, author={Johannes Zierenberg and Niklas Fricke and Martin Marenz and Franz Paul Spitzner and Viktoria Blavatska and Wolfhard Janke}, journal={Physical review. E}, year={2017}, volume={96 6-1}, pages={ 062125 } }

We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to…

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