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Preprint in the OpenAI Math release

SLE3 universality for weak finite-range Ising interactions

OpenAI

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 SLE. 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.

open until 1 Jan 2028

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