At every fixed point on the critical Ashkin–Teller line, including the four-state Potts endpoint, the height and both current-cluster collections converge jointly in bounded Jordan domains: the height to a Gaussian free field and the clusters to canonical recursive two-valued local sets of that field, including all nesting depths and the wired boundary cluster.
At every fixed point on the critical Ashkin–Teller line, including the four-state Potts endpoint, the height and both current-cluster collections converge jointly in bounded Jordan domains: the height to a Gaussian free field and the clusters to canonical recursive two-valued local sets of that field, including all nesting depths and the wired boundary cluster.
At every fixed point on the critical Ashkin–Teller line, including the four-state Potts endpoint, the height and both current-cluster collections converge jointly in bounded Jordan domains: the height to a Gaussian free field and the clusters to canonical recursive two-valued local sets of that field, including all nesting depths and the wired boundary cluster.
If correct, proves the coupled field-and-cluster scaling limit across the critical Ashkin–Teller line.
Do critical Ashkin–Teller heights and both current families have the predicted joint continuum limit?
Publication dates and editorial changes.
OpenAI reports a joint Ashkin–Teller height-and-current limit
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