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The joint scaling limit of critical Ashkin–Teller currents

OpenAI · September 25, 2026

Earlier edition

This is an earlier edition (September 25, 2026). Current edition: The joint scaling limit of critical Ashkin-Teller currents, October 6, 2026.

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@misc{OAI:The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-September-25-2026,
  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-September-25-2026/main.pdf}{OAI:The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-September-25-2026}},
  year = {2026}
}

Family 233: The joint critical Ashkin–Teller current limit

Identifies the joint scaling limit of Ashkin–Teller heights and both complete current-cluster collections throughout the critical line, including the four-state Potts endpoint. In bounded Jordan domains with admissible lattice approximations and wired primal/free dual boundaries, the height converges to the predicted Gaussian free field, and the clusters to canonical recursive sets of that same field, retaining every nesting depth.

This is the only paper in this family.