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The multifractality of the critical eigenstate at the metal to insulatortransition (MIT) in the three-dimensional Anderson model of localization ischaracterized by its associated singularity spectrum f(alpha). Recent works in1D and 2D critical systems have suggested an exact symmetry relation inf(alpha). Here we show the validity of the symmetry at the Anderson MIT withhigh numerical accuracy and for very large system sizes. We discuss thenecessary statistical analysis that supports this conclusion. We have obtainedthe f(alpha) from the box- and system-size scaling of the typical average ofthe generalized inverse participation ratios. We show that the best symmetry inf(alpha) for typical averaging is achieved by system-size scaling, following astrategy that emphasizes using larger system sizes even if this necessitatesfewer disorder realizations.

Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging