We point out that the universality and precision of the Hall plateaus of ${\rho }_H^{\mathrm{-}1}$ in the quantum Hall effect (QHE) can be understood if the conducting component of the two-dimensional electron gas is behaving like a degenerate, intensely magnetized ideal electron gas, whose exact equations of state enforce precisely this behavior. The ideal gas even gives a good description of the QHE behavior outside the plateaus: the spikes of the longitudinal resistivity ρ and the various ‘‘slope’’ and ‘‘minimum’’ relations connect ${\rho }_H$ and ρ, where it might not have been expected. Localization and delocalization of electrons in the QHE occur automatically in the ideal gas as its electrons pass into and out of a thermodynamic particle reservoir. However, renormalization of critical exponents is beyond the scope of this approximation.

• Received 1 June 1989

DOI:https://doi.org/10.1103/PhysRevB.41.2229