{"id":"openai-math/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model","pdf":"https://github.com/openai/math/blob/main/preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Essential-Singularity-of-the-Correlation-Length-in-the-Planar-XY-Model-October-5-2026","tags":["statistical-mechanics","xy-model","phase-transitions"],"score":0,"title":"Essential Singularity of the Correlation Length 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":"We prove the Berezinskii–Kosterlitz–Thouless essential singularity for the correlation length of the nearest-neighbor cosine XY model on the square lattice. Let $`m(b)`$ be the mass obtained by taking first the free-box thermodynamic limit and then the separation limit along a coordinate axis. As the inverse temperature b approaches b c from the massive side, $`\\displaystyle \\sqrt{b_c-b}\\log\\frac{1}{m(b)} \\longrightarrow A_{\\mathrm{XY}},`$ 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"}