Super-Universality in Anderson Localization

Abstract

We calculate the effective spatial dimension $d_{\text{IR}}$ of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value $d_{\text{IR}}=2.665(3)\approx 8/3$. The existence of such a unique marker may help identify natural processes driven by Anderson localization, and provide new insight into the spatial geometry of Anderson transitions. The recently introduced $d_{\text{IR}}$ is a measure-based dimension of Minkowski/Hausdorff type, designed to characterize probability-induced effective subsets.

arXiv comment5 pages, 2 figures; v2: minor changes, published version

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