2008/07/14 by Louella Vasquez, Louella J. Vasquez, Alberto Rodriguez +3 · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.78.195106
published as Phys. Rev. B 78, 195106 (2008) · 10 pages, 12 figures
arxiv created 2008/07/14 · openalex publication_date 2008/11/10 · arxiv updated 2009/12/01 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28
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(\ensuremathα). Recent works in one-dimensional and two-dimensional critical systems have suggested an exact-symmetry relation in f(\ensuremathα). 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(\ensuremathα) from the box-size and system-size scalings of the typical average of the generalized inverse participation ratios. We show that the best symmetry in f(\ensuremathα) 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.