The Hasenfratz-Maggiore-Niedermayer exact mass gap for the two-dimensional O(4) lattice model

Theorem 1.1: for the periodic infinite-volume state, the gap of the full Osterwalder-Schrader transfer operator, including rotation-invariant sectors and measured in original lattice time steps, satisfies $\lim_{\beta\to\infty}e^{\pi\beta}\beta^{-1/2}m_{\mathrm{lat}}(\beta)=32\exp(\pi/4-1/2)$ . The input companion gives $c\sqrt\beta e^{-\pi\beta}\le m_{\mathrm{lat}}\le C\sqrt\beta e^{-\pi\beta}$ and a positive full gap at every $\beta>0$ . Not shown: the corresponding exact constant for $O(3)$ or general $O(n)$ , a continuum $O(4)$ theory, or any statement about nonperiodic Gibbs states.

Exact FrontierDelta

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Occurred: Oct 5, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Hasenfratz-Maggiore-Niedermayer exact mass gap for the two-dimensional O(4) lattice model · Exact O(4) mass gap asymptotics

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VibeMathed record: The Hasenfratz-Maggiore-Niedermayer exact mass gap for the two-dimensional O(4) lattice model

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 and the historical section of 'Exact mass asymptotics for the two-dimensional O(4) lattice model' were read against the Hasenfratz-Maggiore-Niedermayer prediction as the paper cites it. The constant 32 exp(pi/4 - 1/2) was not independently re-derived from the MS-bar ratio here. The proof (sector comparison, a Brownian U(2) regulator solved by Bethe-type integral equations, and regulator matching with a finite coupling shift) was not refereed. No Lean formalization: the family's Lean scope note excludes the O(4) gap claims. The result depends on the unreviewed companion 'Sharp mass bounds' for the two-sided bounds, the periodic state and the renormalization trajectories, and on two O(3) companions for adapted arguments.

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The Hasenfratz-Maggiore-Niedermayer exact mass gap for the two-dimensional O(4) lattice model

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Input: Sharp mass bounds for the two-dimensional O(4) model

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Hasenfratz, Maggiore, Niedermayer 1990, Phys. Lett. B

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The Hasenfratz-Maggiore-Niedermayer exact mass gap for the two-dimensional O(4) lattice model evidence for this event

Hasenfratz, Maggiore, Niedermayer 1990, Phys. Lett. B evidence for this event

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Input: Sharp mass bounds for the two-dimensional O(4) model evidence for this event

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