# Connection probabilities and RSW-type bounds for the FK Ising model

@article{DuminilCopin2009ConnectionPA, title={Connection probabilities and RSW-type bounds for the FK Ising model}, author={Hugo Duminil-Copin and Cl{\'e}ment Hongler and Pierre Nolin}, journal={arXiv: Probability}, year={2009} }

We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions. Our proof relies mainly on Smirnov's fermionic observable for the FK Ising model, which allows us to get precise estimates on boundary connection probabilities. It remains purely discrete, in particular we do not make use of any continuum limit, and it can be used to derive directly several noteworthy results - some new and some not - among…

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