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We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilitiesfor the FK Ising model at criticality, independent of the boundary conditions.Our proof relies mainly on Smirnov's fermionic observable for the FK Isingmodel, which allows us to get precise estimates on boundary connectionprobabilities. It remains purely discrete, in particular we do not make use ofany continuum limit, and it can be used to derive directly several noteworthyresults - some new and some not - among which the fact that there is nospontaneous magnetization at criticality, tightness properties for theinterfaces, and the existence of several critical exponents, in particular thehalf-plane one-arm exponent.

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