oai-math-revised beta

Browse › Probability and statistical mechanics › 218 Conformal universality for weakly interacting and random-bond Ising models

SLE3 universality for weak finite-range Ising interactions

OpenAI · September 23, 2026

Lean

Open PDFCite Report a problem Add a reference or comment Interested in working on this Start a discussion

Edit NOTES.md · Existing issues · Source on GitHub

Abstract

We prove that every sufficiently small, square-symmetric finite-range perturbation of the planar Ising contour energy has a domain-independent inverse temperature at which its spin interface converges to chordal SLE3. The result allows interactions of either sign, arbitrary admissible exterior contours, and uniformly approximated Jordan domains. Convergence holds for the full oriented curve law in uniform distance modulo increasing reparametrization.

If the PDF does not display here, open it directly: Open PDF.

Notes

No notes yet. Add a reference, a comment or your name with the buttons above, or edit NOTES.md on GitHub.

Automatically collected notes (unreviewed)

work in progress

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 uses as an input; the SLE₃ theorem itself is not formalized. [family-level]

Digests and expositions

Elsewhere

Independent sites; their content is not reviewed here.

Cite

@misc{OAI:SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026,
  author = {{OpenAI}},
  title = {{$\mathrm{SLE}_3$ universality for weak finite-range Ising interactions}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026/paper.pdf}{OAI:SLE3-universality-for-weak-finite-range-Ising-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.

Other papers in this family: