Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

Abstract

We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.

10 pages, 13 figures

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Cited by in corpus (4)

• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Multifractality of ab initio wave functions in doped semiconductors
• Multifractal analysis of electronic states on random Voronoi-Delaunay lattices
• Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices