{"id":"openai-math/The-Critical-Spin-Field-of-the-Planar-XY-Model","pdf":"https://github.com/openai/math/blob/main/preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Critical-Spin-Field-of-the-Planar-XY-Model-October-5-2026","tags":["statistical-mechanics","xy-model","gaussian-free-field"],"score":0,"title":"The Critical Spin Field of the Planar XY Model","domain":"Probability and statistical mechanics","family":"216","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"Using the companion critical Bessel-height and pin-limit theorems, we prove that at the mass-defined critical inverse temperature of the nearest-neighbor XY model on the square lattice, the spin field on a square with boundary angles fixed to zero converges along the full sequence to the full-variance imaginary exponential of a zero-Dirichlet Gaussian free field with stiffness $`2/\\pi`$. The normalization uses the exact center magnetization and the lattice Green-function factor. Convergence holds in law in $`H^{-3}_{\\mathrm{loc}}((-1,1)^2)`$; all mixed moments and joint laws of fields…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Critical and near-critical XY scaling and BKT universality"}