  We consider the Ising model at its critical temperature with external
magnetic field $ha^{15/8}$ on $a\mathbb{Z}^2$. We give a purely probabilistic
proof, using FK methods rather than reflection positivity, that for $a=1$, the
correlation length is $\geq const.~h^{-8/15}$ as $h\downarrow0$. We extend to
the $a\downarrow0$ continuum limit the FK-Ising coupling for all $h>0$, and
obtain tail estimates for the largest renormalized cluster area in a finite
domain as well as an upper bound with exponent $1/8$ for the one-arm event.
Finally, we show that for $a=1$, the average magnetization, $\mathcal{M}(h)$,
in $\mathbb{Z}^2$ satisfies $\mathcal{M}(h)/h^{1/15}\rightarrow$ some
$B\in(0,\infty)$ as $h\downarrow0$.
