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Scaling law and critical exponent for alpha_0 at the 3D Anderson transition

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Vasquez, Louella J., Slevin, Keith, Rodriguez, A. (Alberto) and Roemer, Rudolf A.. (2009) Scaling law and critical exponent for alpha_0 at the 3D Anderson transition. Annalen der Physik, Vol.18 (No.12). pp. 901-904. ISSN 0003-3804

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Official URL: http://dx.doi.org/10.1002/andp.200910397

Abstract

We use high-precision, large system-size wave function data to analyse the scaling properties of the multifractal
spectra around the disorder-induced three-dimensional Anderson transition in order to extract the
critical exponents of the transition. Using a previously suggested scaling law, we find that the critical exponent
is significantly larger than suggested by previous results. We speculate that this discrepancy is due
to the use of an oversimplified scaling relation.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics
Q Science > QC Physics

Divisions:

Faculty of Science > Centre for Scientific Computing
Faculty of Science > Physics

Library of Congress Subject Headings (LCSH):

Localization theory -- Research, Multifractals -- Research, Scaling laws (Statistical physics), Exponents (Algebra)

Journal or Publication Title:

Annalen der Physik

Publisher:

Wiley - VCH Verlag GmbH & Co. KGaA

ISSN:

0003-3804

Official Date:

December 2009

Dates:

Date	Event
December 2009	Published

Volume:

Vol.18

Number:

No.12

Page Range:

pp. 901-904

Identification Number:

10.1002/andp.200910397

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Description:

Originally published in the December 2009 issue of Annalen der Physik; revised 08 June 2010.

Funder:

Engineering and Physical Sciences Research Council (EPSRC), Ōsaka Daigaku (OD)

Grant number:

EP/C007042/1 (EPSRC)

References:

[1] R. A. R¨omer and M. Schreiber, The Anderson Transition and its Ramifications — Localisation, Quantum Interference,
and Interactions, Lecture Notes in Physics, Vol. 630, (Springer, Berlin, 2003), chap. Numerical
investigations of scaling at the Anderson transition, pp. 3–19.
[2] F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80(October), 1355–1417 (2008).
[3] K. Slevin and T. Ohtsuki, Phys. Rev. Lett. 82, 382–385 (1999), ArXiv: cond-mat/9812065.
[4] F. Milde, R. A. R¨omer, and M. Schreiber, Phys. Rev. B 61, 6028–6035 (2000), ArXiv: cond-mat/9909210.
[5] L. J. Vasquez, A. Rodriguez, and R. A. R¨omer, Eur. Phys. J. B (2008).
[6] L. J. Vasquez, A. Rodriguez, and R. A. R¨omer, Phys. Rev. B 78, 195106 (2008), cond-mat:0807.2217v1.
[7] A. Rodriguez, L. J. Vasquez, and R. A. R¨omer, Phys. Rev. B 78, 195107 (2008), cond-mat:0807.2209v1.
[8] A. Rodriguez, L. J. Vasquez, and R. A. R¨omer, Phys. Rev. Lett. 102, 106406 (2009), cond-mat:0812.1654.
[9] M. Janssen, Int. J. Mod. Phys. B 8, 943 (1994).
[10] B. Huckestein and L. Schweitzer, Physica A 191, 406–409 (1992).
[11] F. Wegner, Nucl. Phys. B 316, 663–678 (1989).

URI:

http://wrap.warwick.ac.uk/id/eprint/3233

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