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Multifractal finite-size scaling and universality at the Anderson transition
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Rodriguez, A. (Alberto), Vasquez, Louella J., Slevin, Keith and Roemer, Rudolf A.. (2011) Multifractal finite-size scaling and universality at the Anderson transition. Physical Review B (Condensed Matter and Materials Physics), Vol.84 (No.13). article no. 134209 . ISSN 1098-0121
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Official URL: http://dx.doi.org/10.1103/PhysRevB.84.134209
Abstract
We describe a new multifractal finite-size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L3=1203 and involving nearly 106 independent wave functions have yielded unprecedented precision for the critical disorder Wc=16.530(16.524,16.536) and the critical exponent ν=1.590(1.579,1.602). We find that the multifractal exponents Δq exhibit a previously predicted symmetry relation and we confirm the nonparabolic nature of their spectrum. We explain in detail the MFSS procedure first introduced in our Letter [ Phys. Rev. Lett. 105 046403 (2010)] and, in addition, we show how to take account of correlations in the simulation data. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QC Physics |
| Divisions: | Faculty of Science > Centre for Complexity Science Faculty of Science > Physics Faculty of Science > Centre for Scientific Computing Faculty of Science > Statistics |
| Library of Congress Subject Headings (LCSH): | Multifractals, Anderson model, Fluctuations (Physics), Wave functions |
| Journal or Publication Title: | Physical Review B (Condensed Matter and Materials Physics) |
| Publisher: | American Physical Society |
| ISSN: | 1098-0121 |
| Date: | 2011 |
| Volume: | Vol.84 |
| Number: | No.13 |
| Number of Pages: | 6 |
| Page Range: | article no. 134209 |
| Identification Number: | 10.1103/PhysRevB.84.134209 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Spanish Government, Ōsaka Daigaku [Osaka University] |
| Grant number: | EP/F32323/1 (EPSRC), EP/C007042/1 (EPSRC), EP/D065135/1 (EPSRC), FIS2009-07880 (SG) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/40112 |
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