Does a magnetic field modify the critical behaviour at the metal-insulator transition in 3-dimensional disordered systems?

TL;DR

This study investigates how magnetic fields influence the critical behavior of the metal-insulator transition in 3D disordered systems, revealing that the critical point's spectral statistics are unaffected by magnetic fields.

Contribution

It demonstrates that the critical spectral statistics at the transition are independent of magnetic fields, highlighting the role of symmetry at the critical point.

Findings

Different level statistics on metallic and insulating sides

Critical point statistics are magnetic field independent

Critical behavior depends on system symmetry at transition

Abstract

The critical behaviour of 3-dimensional disordered systems with magnetic field is investigated by analyzing the spectral fluctuations of the energy spectrum. We show that in the thermodynamic limit we have two different regimes, one for the metallic side and one for the insulating side with different level statistics. The third statistics which occurs only exactly at the critical point is {\it independent} of the magnetic field. The critical behaviour which is determined by the symmetry of the system {\it at} the critical point should therefore be independent of the magnetic field.