PDE and mathematical physics · Oct 6, 2026

Canonical $O(3)$ continuum limit and exact $O(4)$ mass asymptotics

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)\sim32e^{\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 ≥ 3 at every positive temperature.

Contributors

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AI systems: Unreleased OpenAI model