Family 225Probability and statistical mechanicsNo LeanNot yet digested
Gaussian free field limits throughout the balanced six-vertex regime
The balanced square-lattice six-vertex height field with and 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 , the exact variance multiplier is .
Manuscripts in this family · 1
The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)
Sep 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
We prove that the height function of the square-lattice six-vertex model with weights and , in the plane state obtained from balanced tori, converges to a multiple of the Gaussian free field. For unit height jumps and Green kernel , the squared multiplier is .