  A sharp-threshold theorem is proved for box-crossing probabilities on the
square lattice. The models in question are the random-cluster model near the
self-dual point $p_{\mathrm {sd}}(q)=\sqrt{q}/(1+\sqrt{q})$, the Ising model
with external field, and the colored random-cluster model. The principal
technique is an extension of the influence theorem for monotonic probability
measures applied to increasing events with no assumption of symmetry.
