Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-07-14
Phys. Rev. B 78, 195106 (2008)
Physics
Condensed Matter
Disordered Systems and Neural Networks
10 pages, 12 figures
Scientific paper
10.1103/PhysRevB.78.195106
The multifractality of the critical eigenstate at the metal to insulator transition (MIT) in the three-dimensional Anderson model of localization is characterized by its associated singularity spectrum f(alpha). Recent works in 1D and 2D critical systems have suggested an exact symmetry relation in f(alpha). Here we show the validity of the symmetry at the Anderson MIT with high numerical accuracy and for very large system sizes. We discuss the necessary statistical analysis that supports this conclusion. We have obtained the f(alpha) from the box- and system-size scaling of the typical average of the generalized inverse participation ratios. We show that the best symmetry in f(alpha) for typical averaging is achieved by system-size scaling, following a strategy that emphasizes using larger system sizes even if this necessitates fewer disorder realizations.
Rodriguez Alberto
Roemer Rudolf A.
Vasquez Louella J.
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