PDE and mathematical physics · Oct 6, 2026

Gaussian free field limits throughout the balanced six-vertex regime

The balanced square-lattice six-vertex height field with a=b=1a=b=1 and 0<c≤20\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 −(2π)−1log⁡∣x−y∣-(2\pi)^{-1}\log|x-y|, the exact variance multiplier is 1/arcsin⁡(c/2)1/\arcsin(c/2).

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