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Super-Universality in Anderson Localization
Ivan Horváth1,2, Peter Markoš3
1University of Kentucky, Lexington, Kentucky 40506, USA.
Abstract:
We calculate the effective spatial dimension d_{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_{IR}=2.665(3)≈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_{IR} is a measure-based dimension of Minkowski-Hausdorff type, designed to characterize probability-induced effective subsets.
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