Universal Singularities in the Integral Quantum Hall Effect

The transition between localized and extended eigenstates in the integral quantum Hall regime is observable as a scaling phenomenon in the magnetoresistance tensor as a function of temperature and applied magnetic field strength. Field-theoretic studies on the quantum Hall effect are used to derive the scaling functions. The scaling behavior is shown to involve only a single critical exponent (μ) which is the ratio between the inelastic-scattering exponent (p) and twice the localization length exponent (ν). The results have recently been confirmed experimentally.