  We prove that for the Ising model defined on the plane $\Z^2$ at
$\beta=\beta_c$, the average magnetization under an external magnetic field
$h>0$ behaves exactly like \[{\sigma_0}_{\beta_c, h} \asymp h^{\frac 1 {15}}\,.
\] The proof, which is surprisingly simple compared to an analogous result for
percolation (i.e. that $\theta(p)=(p-p_c)^{5/36+o(1)}$ on the triangular
lattice \cite{\SmirnovWerner,\KestenScaling}) relies on the GHS inequality as
well as the RSW theorem for FK percolation from \cite{\RSWfk}. The use of GHS
to obtain inequalities involving critical exponents is not new; in this paper
we show how it can be combined with RSW to obtain matching upper and lower
bounds for the average magnetization.
