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 (2009)] to yield the most reliable results.
Similar content being viewed by others
References
C. Castellani, L. Peliti, J. Phys. A 19, L429 (1986)
M. Schreiber, H. Grussbach, Phys. Rev. Lett. 67, 607 (1991)
H. Böttger, G. Kasner, Phys. Stat. Sol. B 162, 489 (1990)
A. Chhabra, R.V. Jensen, Phys. Rev. Lett. 62, 1327 (1989)
A. Rodriguez, L.J. Vasquez, R.A. Römer, Phys. Rev. B 78, 195107 (2008)
B. Huckestein, R. Klesse, Phys. Rev. B 55, 7303 (1997)
A. Rodriguez, L.J. Vasquez, R.A. Römer, Eur. Phys. J. B 67, 77 (2009)
H. Grussbach, M. Schreiber, Chem. Phys. 177, 733 (1993)
M. Schreiber, in Computational Physics: Selected Methods – Simple Exercises – Serious Applications, edited by K.H. Hoffmann, M. Schreiber (Springer, Berlin, Heidelberg, 1996), p. 147
M. Bollhöfer, Y. Notay, Comput. Phys. Commun. 177, 951 (2007)
T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Phys. Rev. A 33, 1141 (1986)
J. Feder, Fractals (Plenum, New York, 1988)
M. Janssen, Int. J. Mod. Phys. B 8, 943 (1994)
L.J. Vasquez, A. Rodriguez, R.A. Römer, Phys. Rev. B 78, 195106 (2008)
M. Schreiber, H. Grussbach, Philosophical Magazine B 65, 707 (1992)
A. Rodriguez, L.J. Vasquez, K. Slevin, R.A. Römer, Phys. Rev. B 84, 134209 (2011)
H. Grussbach, M. Schreiber, Phys. Rev. B 51, 663 (1995)
F. Milde, R.A. Römer, M. Schreiber, Phys. Rev. B 55, 9463 (1997)
W. Pook, M. Janssen, Z. Phys. B 82, 295 (1991)
M. Schreiber, F. Milde, R.A. Römer, Comput. Phys. Commun. 121–122, 517 (1999)
A.D. Mirlin, Y.V. Fyodorov, A. Mildenberger, F. Evers, Phys. Rev. Lett. 97, 046803 (2006)
A. Rodriguez, L.J. Vasquez, R.A. Römer, Phys. Rev. Lett. 102, 106406 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Thiem, S., Schreiber, M. Partitioning schemes and non-integer box sizes for the box-counting algorithm in multifractal analysis. Eur. Phys. J. B 86, 48 (2013). https://doi.org/10.1140/epjb/e2012-30410-x
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2012-30410-x