Eur. Phys. J. B 67, 77-82 (2009)
https://doi.org/10.1140/epjb/e2009-00009-7

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

¹ Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, UK
² Departamento de Fisica Fundamental, Universidad de Salamanca, 37008 Salamanca, Spain

Corresponding author: ^a L.J.A.Vasquez@warwick.ac.uk

Received: 30 July 2008
Revised: 15 October 2008
Published online: 13 January 2009

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.