Niklas Fricke

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

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 such system details. By contrast, we verify that the fractal dimension d_{f} is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching d_{f}→2. The onset of this change does not seem to be determined by the extended Harris criterion.

Scaling laws for random walks in long-range correlated disordered media

We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the distance as a power law,

Polymers in disordered environments

r^{-a}

Scale-free enumeration of self-avoiding walks on critical percolation clusters

, generated with the improved Fourier filtering method. To characterize this type of disorder, we determine the percolation threshold

Asymptotic scaling behavior of self-avoiding walks on critical percolation clusters.

p_{\text c}

Exact enumeration of self-avoiding walks on critical percolation clusters in two to seven dimensions

by investigating cluster-wrapping probabilities. At

Exact enumeration of self-avoiding walks on critical percolation clusters in 2–7 dimensions

p_{\text c}

Erratum: Asymptotic Scaling Behavior of Self-Avoiding Walks on Critical Percolation Clusters [Phys. Rev. Lett. 113, 255701 (2014)].

, we estimate the (sub-diffusive) walk dimension

Diffusion and polymers in fractal, disordered environments

d_{\text w}

Diffusion and self-avoiding walks on percolation clusters

for different correlation exponents