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Quenched SLE Universality for Weakly Disordered FK–Ising Interfaces
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Abstract
We prove that critical FK–Ising interfaces with sufficiently weak, symmetric, independent two-valued bond disorder converge to chordal SLE16/3. The disorder strength is fixed as the mesh tends to zero, and convergence of the conditional curve laws holds in probability over the environment.
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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.
Possibly relevant literature (found by the agent, not checked)
- Yu Feng, Eveliina Peltola and Hao Wu, Connection probabilities of multiple FK-Ising interfaces (Probability Theory and Related Fields 189, 281–367, 2024). Provides homogeneous critical FK–Ising connection-probability formulas relevant to the pure-model four-point tests used in this manuscript’s quenched argument.
Digests and expositions
- Latent Seminar, Random-cluster curves: conformal limits and natural time (6 October 2026). Discusses conditional interface tests after exploration in a fixed random environment. [family-level]
Elsewhere
- Emergent Mind: family 223
Independent sites; their content is not reviewed here.
Cite
@misc{OAI:Quenched-SLE-Universality-for-Weakly-Disordered-FK-Ising-Interfaces-October-5-2026,
author = {{OpenAI}},
title = {{Quenched SLE Universality for Weakly Disordered FK--Ising Interfaces}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Quenched-SLE-Universality-for-Weakly-Disordered-FK-Ising-Interfaces-October-5-2026/quenched-fk-ising.pdf}{OAI:Quenched-SLE-Universality-for-Weakly-Disordered-FK-Ising-Interfaces-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
- Thermal FK–Ising interfaces and massive SLE · 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