{"id":"openai-math/BKT-universality-for-height-and-planar-spin-fields","pdf":"https://github.com/openai/math/blob/main/preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/BKT-universality-for-height-and-planar-spin-fields-September-24-2026","tags":["statistical-mechanics","kosterlitz-thouless","gaussian-free-field"],"score":0,"title":"BKT universality for height and planar spin fields","domain":"Probability and statistical mechanics","family":"216","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove Gaussian scaling limits for the two-dimensional discrete Gaussian height model throughout its rough phase, including the physical roughening threshold, for every finite square-symmetric interaction set containing the nearest neighbors. After the natural lattice normalization, the critical effective temperature has the universal value $`8\\pi`$. For the ordinary nearest-neighbor Villain and XY models at sufficiently low fixed temperatures, we also prove that their Green-function-normalized spin fields converge to the imaginary exponential of a Dirichlet Gaussian free field.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Critical and near-critical XY scaling and BKT universality"}