{"id":"openai-math/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2","pdf":"https://github.com/openai/math/blob/main/preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026","tags":["statistical-mechanics","six-vertex-model","gaussian-free-field","integrable-systems"],"score":0,"title":"The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)","domain":"Probability and statistical mechanics","family":"225","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that the height function of the square-lattice six-vertex model with weights $`a=b=1`$ and $`0\\lt c\\le2`$, in the plane state obtained from balanced tori, converges to a multiple of the Gaussian free field. For unit height jumps and Green kernel $`-(2\\pi)^{-1}\\log|x-y|`$, the squared multiplier is $`1/\\arcsin(c/2)`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Gaussian free field limits throughout the balanced six-vertex regime"}