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Title: Critical exponents of the quantum Hall transition with Coulomb interaction
Plain: Real quantum Hall transitions involve repelling electrons, which changes how time and length scale near the transition. Experiments measure a combined exponent of about 0.42, but theory has not computed it with the repulsion included.
Precise: AlGaAs/GaAs plateau transitions give $\kappa=1/(z\nu)\sim 0.42$ (Li et al. 2009), with $z\sim 1$ as expected for $1/r$ interaction. Short-range interactions are irrelevant at the non-interacting fixed point, while $1/r$ Coulomb interaction is relevant. Compute $\nu\ \text{and}\ z$ at the interacting fixed point and decide whether $\nu$ equals the non-interacting value.
Settled by: A controlled calculation (Hartree-Fock network models, sigma-model renormalization, or exact methods on large interacting systems) giving $\nu\text{ and }z$ with error bars, compared with temperature- and frequency-scaling experiments.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)