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Thermal FK–Ising interfaces and massive SLE
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Abstract
We prove convergence of thermal FK–Ising interfaces, for every fixed nonzero mass of either sign, on uniformly angle-bounded isoradial lattices in bounded simply connected domains. The limit is independent of the lattice and the admissible domain approximation. For positive mass it is the unique massive SLE$_{16/3}$ law with locally finite-energy drift prescribed by a massive boundary value problem; negative mass follows by duality and reversal. The theorem also allows Carathéodory approximations whose diameters diverge.
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Possibly relevant literature (found by the agent, not checked)
- Hugo Duminil-Copin, Christophe Garban and Gábor Pete, The near-critical planar FK-Ising model (arXiv:1111.0144; Comm. Math. Phys. 326 (2014)). Determines the near-critical FK-Ising correlation length through crossing probabilities, which is relevant to the paper's thermal (mass-scaled) FK-Ising regime; not cited in the paper.
- Dmitry Chelkak, Konstantin Izyurov and Rémy Mahfouf, Universality of spin correlations in the Ising model on isoradial graphs (arXiv:2104.12858, 2021). Proves lattice-independent massive scaling limits on isoradial graphs via discrete massive holomorphic spinors, which parallels this paper's claim that the massive limit does not depend on the isoradial lattice.
Digests and expositions
- Latent Seminar, Random-cluster curves: conformal limits and natural time (6 October 2026). Outlines the claimed finite-energy drift and stopped-change-of-measure uniqueness argument. [family-level]
News and blogs
- David Holmes’s website, New definitions in the OpenAI math papers (14 October 2026). This explicitly AI-produced comparison discusses the thermal paper’s massive SLE definition in relation to Makarov–Smirnov’s program and states that no proofs were checked. [AI-generated per source]
Elsewhere
- Emergent Mind: family 223
Independent sites; their content is not reviewed here.
Cite
@misc{OAI:Thermal-FK-Ising-interfaces-and-massive-SLE-October-5-2026,
author = {{OpenAI}},
title = {{Thermal FK--Ising interfaces and massive SLE}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Thermal-FK-Ising-interfaces-and-massive-SLE-October-5-2026/paper.pdf}{OAI:Thermal-FK-Ising-interfaces-and-massive-SLE-October-5-2026}},
year = {2026}
}Family 223: Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling
Proves chordal SLEκ limits for critical square-lattice random-cluster interfaces for $0\lt q\le4$, with $\kappa=4\pi/\arccos(-\sqrt q/2)$: bounded Jordan domains are allowed for q ≥ 1, and smooth Jordan domains for q < 1, under the stated marked-boundary approximations. For $1\le q\le4$, complete nested plane loops converge to CLEκ.
Other papers in this family:
- Square-lattice FK interfaces and nested loops for 1 <= q < 4 · September 23, 2026
- Self-dual random-cluster interfaces below one · September 23, 2026
- Quenched SLE Universality for Weakly Disordered FK–Ising Interfaces · October 5, 2026
- Natural Occupation Measures for Critical Square-Lattice FK Interfaces · October 5, 2026
- Conformal Limits of Critical Square-Lattice Random-Cluster Interfaces · October 5, 2026