Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 215-05. Exponential decay in two-dimensional classical O(n) models
Manuscript map · lines 6315–6324
OpenAI@2026-10-07#rem:oai-p-215-05
Authors: OpenAI. Family 215.
Title: Exponential decay in two-dimensional classical O(n) models.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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