{"id":"openai-math/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale","pdf":"https://github.com/openai/math/blob/main/preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026","tags":["spin-glass","sherrington-kirkpatrick","statistical-physics","probability"],"score":0,"title":"The low-temperature Sherrington–Kirkpatrick fluctuation scale","domain":"Probability and statistical mechanics","family":"217","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For the zero-field Gaussian Sherrington–Kirkpatrick model at every fixed inverse temperature β > 1, we prove that the standard deviation of the log partition function is $`n^{1/6+o(1)}`$. The same exponent describes its typical centered absolute fluctuations, establishing the predicted one-sixth exponent in this regime.","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"}