Super-Universality in Anderson Localization

TL;DR

This paper investigates the effective spatial dimension at critical points of 3D Anderson models across various universality classes, revealing a super-universal value that enhances understanding of Anderson transitions.

Contribution

It introduces and calculates a super-universal effective spatial dimension for Anderson localization, applicable across multiple universality classes, providing a new geometric marker for Anderson transitions.

Findings

Effective spatial dimension d_IR ≈ 8/3 across classes

Supports super-universality of Anderson transition geometry

Provides a new measure-based dimension for localization analysis

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.