{"id":"openai-math/The-critical-correlation-exponent-of-the-planar-XY-model","pdf":"https://github.com/openai/math/blob/main/preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-critical-correlation-exponent-of-the-planar-XY-model-September-24-2026","tags":["statistical-mechanics","xy-model","bkt-transition","critical-phenomena"],"score":0,"title":"The critical correlation exponent 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":"For the ordinary nearest-neighbor XY model on the square lattice, we prove the Berezinskii–Kosterlitz–Thouless prediction that the critical spin-correlation exponent is 1/4. More precisely, at the mass-defined critical inverse temperature, the infinite-volume correlation is $`n^{-1/4+o(1)}`$. The infinite-volume limit through free square boxes is taken before the separation limit.","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"}