Charged particles in random magnetic fields and the critical behavior in the fractional quantum Hall effect

TL;DR

This paper investigates the critical behavior of non-interacting charged particles in random magnetic fields, proposing a universality class shared with the integer Quantum Hall effect, supported by analytical and statistical evidence.

Contribution

It demonstrates the universality of critical behavior in the fractional Quantum Hall effect model across various Landau levels and magnetic field fluctuations.

Findings

Universality class matches that of the integer Quantum Hall effect.

Proven for lowest Landau level and slowly fluctuating magnetic fields.

Supported by analysis of a related random matrix model.

Abstract

As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model belongs to the same universality class as the integer Quantum Hall effect. The universality is proved for the limiting cases of the lowest Landau level, and slowly fluctuating magnetic fields in arbitrary Landau levels. The conjecture that the universality holds in general is based on the study of the statistical properties of the corresponding random matrix model.