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Optimisation of multifractal analysis at the 3D Anderson transition using box-size scaling

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Rodriguez, A. (Alberto), Vasquez, Louella J. and Roemer, Rudolf A.. (2009) Optimisation of multifractal analysis at the 3D Anderson transition using box-size scaling. European Physical Journal B. Condensed Matter and Complex Systems, Vol.67 (No.1). pp. 77-82. ISSN 1434-6028

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Abstract

We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(alpha), of the critical eigenstates at the metal-insulator transition within the 3-D Anderson model of localisation. The typical and ensemble averaged scaling laws of the generalised inverse participation ratios are considered. In pursuit of a numerical optimisation of the box-scaling technique we discuss different box-partitioning schemes including cubic and non-cubic boxes, use of periodic boundary conditions to enlarge the system and single and multiple origins for the partitioning grid are also implemented. We show that the numerically most reliable method is to divide a system of linear size L equally into cubic boxes of size l for which L/l is an integer. This method is the least numerically expensive while having a good reliability.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Q Science > QD Chemistry
Divisions: Faculty of Science > Physics
Faculty of Science > Centre for Scientific Computing
Library of Congress Subject Headings (LCSH): Metal-insulator transitions, Anisotropy, Scaling laws (Statistical physics), Anderson model, Fluctuations (Physics)
Journal or Publication Title: European Physical Journal B. Condensed Matter and Complex Systems
Publisher: EDP Sciences
ISSN: 1434-6028
Official Date: January 2009
Volume: Vol.67
Number: No.1
Number of Pages: 6
Page Range: pp. 77-82
Identification Number: 10.1140/epjb/e2009-00009-7
Status: Peer Reviewed
Publication Status: Published
Funder: Engineering and Physical Sciences Research Council (EPSRC), Spanish Government, Castilla y León (Spain). Junta
Grant number: EP/C007042/1 (EPSRC), JC2007-00303 (SG), FIS2006-00716 (SG), MMA-A106/2007 (SG), SA052A07 (JCyL)
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URI: http://wrap.warwick.ac.uk/id/eprint/28541

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