{"id":"openai-math/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law","pdf":"https://github.com/openai/math/blob/main/preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026","tags":["spin-glass","sherrington-kirkpatrick","limit-theorems","probability"],"score":0,"title":"The low-temperature Sherrington–Kirkpatrick free-energy limiting law","domain":"Probability and statistical mechanics","family":"217","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For every fixed inverse temperature β > 1, we prove that the zero-field Gaussian Ising Sherrington–Kirkpatrick free energy, centered by its expectation and divided by its standard deviation, converges in distribution to a nondegenerate law as the system size tends to infinity through all integers. We also prove that its variance divided by n 1/3 converges to a finite positive constant.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The low-temperature Sherrington–Kirkpatrick fluctuation law"}