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Conformal universality of bulk Ising correlations under weak interactions

OpenAI · September 23, 2026

Lean

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Abstract

We prove conformal universality of mixed bulk spin and energy correlations for the square-lattice Ising model with sufficiently small, square-symmetric, finite-range even multispin perturbations of either sign. One critical-temperature branch and two field normalizations apply in every bounded simply connected C2 Jordan domain with free, plus, or minus boundary conditions, and in the periodic thermodynamic plane state. Energies are centered in their actual states.

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Collected automatically by AI tools (Claude Opus 5.5 and GPT-6 Astra, 2026-10-21) and not checked by a person. May be wrong or incomplete. Report an error.

Formalization

  • OpenAI math release, Lean scope note for family 218 (lean/docs/218.md, October 2026). Formalizes only the finite-graph buffered likelihood comparison from the companion Buffered comparison and stopping-band resolution in critical Ising, which this paper cites as an input; the paper's own theorem is not formalized. [family-level]

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Cite

@misc{OAI:Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026,
  author = {{OpenAI}},
  title = {{Conformal universality of bulk Ising correlations under weak interactions}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026/paper.pdf}{OAI:Conformal-universality-of-bulk-Ising-correlations-under-weak-interactions-September-23-2026}},
  year = {2026}
}

Lean formalization

OpenAI provides Lean files for this family: lean/docs/218.md. The Lean statements have not been checked by people against the paper's claims.

Family 218: Conformal universality for weakly interacting and random-bond Ising models

Weak finite-range square-symmetric even multispin perturbations of the square-lattice Ising model preserve critical bulk spin and energy limits; weak square-symmetric contour interactions also yield chordal SLE3 interface limits. With sufficiently weak iid bond disorder of any fixed bounded nondegenerate mean-zero law, critical spin interfaces converge to the same law in probability over environments.

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