Numerical study on Anderson transitions in three-dimensional disordered systems in random magnetic fields

TL;DR

This paper numerically investigates Anderson transitions in three-dimensional disordered systems under random magnetic fields, analyzing critical behavior and universality classes through transfer matrix and equation-of-motion methods.

Contribution

It provides a detailed numerical analysis of critical exponents and fractal dimensions in 3D Anderson transitions influenced by random magnetic fields and scalar potentials.

Findings

Critical exponent ν ≈ 1.45 with strong scalar potential

Exponent varies with system size without scalar potential

Results support universality class classification based on symmetry

Abstract

The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent $\nu$ for the localization length to be $1.45 \pm 0.09$ with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.