{"id":"openai-math/Critical-Center-Magnetization-in-the-Planar-XY-Model","pdf":"https://github.com/openai/math/blob/main/preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Critical-Center-Magnetization-in-the-Planar-XY-Model-October-5-2026","tags":["statistical-mechanics","xy-model","critical-phenomena"],"score":0,"title":"Critical Center Magnetization in 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":"Assuming the stated critical-height, local-renormalization, and spin-field inputs from the companion papers, we determine the center magnetization of the planar XY model in a square with aligned boundary spins at its mass-defined critical threshold. As $`n\\to\\infty`$, the magnetization is $`A_{\\mathrm{XY}}n^{-1/8}(\\log n)^{1/16}(1+o(1))`$, where $`A_{\\mathrm{XY}}`$ is a finite, strictly positive model-specific constant.","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"}