Strong RSW estimates for the FK-Ising model on s-embeddings
Abstract
We adapt the 'induction over scales' scheme of Duminil-Copin, Manolescu, and Tassion to the FK-Ising model on s-embeddings. Namely, we prove the existence of crossings of rough topological quadrilaterals with unfavorable boundary conditions, known as 'strong' RSW, under the 'uniformly bounded geometry' assumption (all edge lengths are comparable to 1 and all angles are bounded from below) on the tangential quads that form an s-embedding. This result has a number of standard consequences like quasi-multiplicativity of arm events and fractal properties of the clusters. It can be applied in a variety of setups including near-critical Ising models on regular grids below the correlation length scale by considering appropriate s-embedding thereof.
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BibTeX
@misc{chelkak2026strong,
title = {{Strong RSW estimates for the FK-Ising model on s-embeddings}},
author = {Dmitry Chelkak and Yanqing Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11990},
eprint = {2610.11990},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11990},
}
RIS
TY - UNPB
TI - Strong RSW estimates for the FK-Ising model on s-embeddings
AU - Dmitry Chelkak
AU - Yanqing Wei
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11990
UR - https://arxiv.org/abs/2610.11990
AB - We adapt the 'induction over scales' scheme of Duminil-Copin, Manolescu, and Tassion to the FK-Ising model on s-embeddings. Namely, we prove the existence of crossings of rough topological quadrilaterals with unfavorable boundary conditions, known as 'strong' RSW, under the 'uniformly bounded geometry' assumption (all edge lengths are comparable to 1 and all angles are bounded from below) on the tangential quads that form an s-embedding. This result has a number of standard consequences like quasi-multiplicativity of arm events and fractal properties of the clusters. It can be applied in a variety of setups including near-critical Ising models on regular grids below the correlation length scale by considering appropriate s-embedding thereof.
ER -