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

Zierenberg, J., Fricke, N., Marenz, M., Spitzner, F. P., Blavatska, V., & Janke, W. (2017). Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects. Physical Review E, 96(6): 062125. doi:10.1103/PhysRevE.96.062125.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002E-9B97-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0001-71A3-7
Genre: Journal Article

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 Creators:
Zierenberg, Johannes1, Author              
Fricke, N., Author
Marenz, M., Author
Spitzner, F. P., Author
Blavatska, V., Author
Janke, W., Author
Affiliations:
1Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063286              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2017-12-182017-12
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1103/PhysRevE.96.062125
 Degree: -

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Title: Physical Review E
Source Genre: Journal
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Pages: 11 Volume / Issue: 96 (6) Sequence Number: 062125 Start / End Page: - Identifier: -