OpenAI · 215-05 · 2026-09-23 · Probability and statistical mechanics
Exponential decay in two-dimensional classical O(n) models
preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026
Family 215. Massive continuum limits and exact mass asymptotics for planar models.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Constructs the canonical continuum limit of the two-dimensional nearest-neighbor model: a non-Gaussian local relativistic theory with a unique vacuum and a positive mass gap. For the square-lattice model, determines the exact leading asymptotic of the full transfer gap, . The family also proves exponential spin-correlation decay for two-dimensional nearest-neighbor models with at every positive temperature.
We prove exponential decay of two-point correlations for the classical nearest-neighbor 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.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 215: Canonical continuum limit and exact mass asymptotics. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.