The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)
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 \(1/\arcsin(c/2)\).
Cite
@misc{OAI:The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026,
author = {{OpenAI}},
title = {{The Gaussian free field limit of the balanced six-vertex model with variance multiplier $1/\arcsin(c/2)$}},
howpublished = {OpenAI Math Release preprint
\href{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}{OAI:The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026}},
year = {2026}
}