The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)

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OpenAI Mathopenai-math/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2Sep 23, 2026math.PRAI-generatedscore 0

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 $1/\arcsin(c/2)$.

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