The joint scaling limit of critical Ashkin-Teller currents
For each fixed point on the critical Ashkin–Teller line, including the four-state Potts endpoint, we prove the conjectured joint scaling limit of the height and both current-cluster collections in every bounded Jordan domain, for every admissible polygonal approximation. The height converges to a Gaussian free field with the predicted coupling constant, and the clusters converge to canonical recursive two-valued local sets of that same field. The joint limit includes all nesting depths and the distinguished wired boundary cluster.
This version corrects the transmission and boundary-collar arguments, replaces excursion convergence with a signed-loop-soup/GMC argument tied to the same limiting field, and updates the companion-paper citation; see the previous version.
Cite
@misc{OAI:The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026,
author = {{OpenAI}},
title = {{The joint scaling limit of critical Ashkin--Teller currents}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026/main.pdf}{OAI:The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026}},
year = {2026}
}