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Accepted · first revision · record

Title: Is the integer quantum Hall transition a conventional critical point?
Plain: Between two quantum Hall plateaus, electron states spread out at a single energy, with a size that diverges according to an exponent. Simulations give about 2.6, experiments about 2.4, and the simulated value drifts with system size, so even the type of critical point is in doubt.
Precise: For the Chalker-Coddington network model (class A, non-interacting), finite-size scaling gives $\nu \sim 2.59$ (Slevin and Ohtsuki 2009), but estimates drift with system size; Zirnbauer (2019) proposed a conformal field theory with a marginal perturbation that implies logarithmic corrections. Determine whether the critical point is an ordinary fixed point with finite $\nu$, a fixed point with a marginal operator, or a line of fixed points, and identify its field theory.
Settled by: An exact identification of the critical field theory that reproduces numerically known multifractal spectra and conductance distributions, or numerics on sizes large enough to fix the form of the corrections to scaling.
Kind: well-posed
Answer type: identification
References: (empty)
Literature status: contested
Status note: Numerical studies (2018-2022) found size drifts consistent with marginal scaling, and a 2025 graphene experiment reported non-universal localization behavior across broken-symmetry states (arXiv 2509.20163).
Posed since: 1988