Universality of the metal-insulator transition in three-dimensional disordered systems

TL;DR

This paper confirms that the metal-insulator transition in three-dimensional disordered systems exhibits universal critical behavior, independent of microscopic disorder details, through numerical analysis of wave function scaling properties.

Contribution

It demonstrates the universality of critical exponents and multifractal dimensions across different disorder definitions in 3D disordered systems.

Findings

Critical exponent ν is universal across disorder types.

Multifractal dimensions d_q are independent of microscopic disorder.

Universality holds along the entire critical line separating metallic and insulating phases.

Abstract

The universality of the metal-insulator transition in three-dimensional disordered system is confirmed by numerical analysis of the scaling properties of the electronic wave functions. We prove that the critical exponent $\nu$ and the multifractal dimensions $d_q$ are independent on the microscopic definition of the disorder and universal along the critical line which separates the metallic and the insulating regime.