Disordered systems and the metal-insulator Transition: A super universality class

TL;DR

This paper investigates the critical behavior of three-dimensional disordered systems at the metal-insulator transition, proposing a super universality class that unifies different symmetry cases based on spectral fluctuation analysis.

Contribution

It introduces the concept of a super universality class for disordered systems, showing that critical behavior is independent of initial symmetries and determined by the symmetry at the critical point.

Findings

Critical exponent ν ≈ 1.35 across all symmetry classes

Spectral fluctuations indicate symmetry breaking at the critical point

Critical behavior is governed by the symmetry at the transition

Abstract

The critical behaviour of three-dimensional disordered systems is investigated by analysing the spectral fluctuations of the energy spectrum. Our results suggest that the initial symmetries (orthogonal, unitary and symplectic) are broken by the disorder at the critical point. The critical behaviour, determinedby the symmetry at the critical point, should therefore be independent of the previous invariances and be described by a ``super'' universality class. This result is strongly supported by the fact that we obtain the same critical exponent $\nu \simeq 1.35$ in the three cases: orthogonal, unitary and symplectic.