{"id":"openai-math/The-joint-scaling-limit-of-critical-Ashkin-Teller-currents","pdf":"https://github.com/openai/math/blob/main/preprints/The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-joint-scaling-limit-of-critical-Ashkin-Teller-currents-October-6-2026","tags":["statistical-mechanics","conformal-field-theory","gaussian-free-field","percolation"],"score":0,"title":"The joint scaling limit of critical Ashkin-Teller currents","domain":"Probability and statistical mechanics","family":"233","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":false,"family_title":"The joint critical Ashkin–Teller current limit"}