The European Physical Journal B

, Volume 67, Issue 1, pp 77–82

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

Authors

  • A. Rodriguez
    • Department of Physics and Centre for Scientific ComputingUniversity of Warwick
    • Departamento de Fisica FundamentalUniversidad de Salamanca
    • Department of Physics and Centre for Scientific ComputingUniversity of Warwick
  • R. A. Römer
    • Department of Physics and Centre for Scientific ComputingUniversity of Warwick
Computational Methods

DOI: 10.1140/epjb/e2009-00009-7

Cite this article as:
Rodriguez, A., Vasquez, L. & Römer, R. Eur. Phys. J. B (2009) 67: 77. doi:10.1140/epjb/e2009-00009-7

Abstract

We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(α), 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.

PACS

71.30.+h Metal-insulator transitions and other electronic transitions72.15.Rn Localization effects05.45.Df Fractals

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009