{"id":"openai-math/The-critical-logarithmic-correction-for-the-planar-XY-model","pdf":"https://github.com/openai/math/blob/main/preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-critical-logarithmic-correction-for-the-planar-XY-model-October-5-2026","tags":["statistical-mechanics","xy-model","critical-phenomena","correlation-functions"],"score":0,"title":"The critical logarithmic correction for 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":"We prove the critical logarithmic correction for the nearest-neighbor cosine XY model on the square lattice. Let $`C_{b_c}(r)`$ be the two-point correlation at critical inverse temperature, obtained by taking the free-box thermodynamic limit while the two sites remain r lattice steps apart along a coordinate axis. Then $`\\displaystyle C_{b_c}(r)=B_{\\mathrm{XY}}r^{-1/4}(\\log r)^{1/8}(1+o(1)), \\qquad B_{\\mathrm{XY}}\\in(0,\\infty),`$ as $`r\\to\\infty`$.","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"}