We calculate the effective spatial dimension $d_{\mathrm{IR}}$ 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 $d_{\mathrm{IR}}=2.665(3)\approx 8/3$. 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 $d_{\mathrm{IR}}$ is a measure-based dimension of Minkowski-Hausdorff type, designed to characterize probability-induced effective subsets.

• Received 24 October 2021
• Revised 16 January 2022
• Accepted 15 August 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.106601