{"id":"openai-math/Exponential-decay-in-two-dimensional-classical-On-models","pdf":"https://github.com/openai/math/blob/main/preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026","tags":["statistical-mechanics","spin-models","correlation-decay"],"score":0,"title":"Exponential decay in two-dimensional classical O(n) models","domain":"Probability and statistical mechanics","family":"215","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove exponential decay of two-point correlations for the classical nearest-neighbor $`O(n)`$ model on the square lattice, for every n ≥ 3 and every finite positive inverse temperature. The estimate is uniform over finite free-boundary subgraphs and bounded nonnegative edge strengths. This resolves positively the all-temperature exponential spin-decay conjecture for these models.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Canonical $`O(3)`$ continuum limit and exact $`O(4)`$ mass asymptotics"}