Gaussian free field limits throughout the balanced six-vertex regime

The balanced square-lattice six-vertex height field with a=b=1 and 0\lt c\le2 converges to a Gaussian free field, including at the endpoint c = 2. The plane state is defined by balanced-torus limits. For unit height increments and Green kernel -(2\pi)^{-1}\log|x-y|, the exact variance multiplier is 1/\arcsin(c/2).

Manuscript

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

September 23, 2026 · source · cite as \cite{OAI:The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026}

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).

Result 225 · Probability and statistical mechanics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.