Remark: Family 215. Massive continuum limits and exact mass asymptotics for planar O(n) models

Constructs the canonical continuum limit of the two-dimensional nearest-neighbor $O(3)$ model: a non-Gaussian local relativistic theory with a unique vacuum and a positive mass gap. For the square-lattice $O(4)$ model, determines the exact leading asymptotic of the full transfer gap, $m_{\mathrm{lat}}(\beta )\sim 32e^{\pi /4-1/2}\sqrt{\beta }{e}^{-\pi \beta }$. The family also proves exponential spin-correlation decay for two-dimensional nearest-neighbor $O(n)$ models with $n\ge 3$ at every positive temperature.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.