{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"130b0eb8d5d7f21eb6c4fa11f10078904bb51a6b54d6708207ca6b5c87abae0f","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"b87171134da97baa3296fa93fd8c68820e12667e18fb829209a213e0efee9f49","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.anderson-transitions.iqh-coulomb-exponents","kind":"well-posed","literature_status":"open","n":"1","parents":[],"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.","posed_since":"","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.","problem_ref":null,"references":"","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.","status_note":"","title":"Critical exponents of the quantum Hall transition with Coulomb 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