  In this paper we develop a detailed analysis of critical prewetting in the
context of the two-dimensional Ising model. Namely, we consider a
two-dimensional nearest-neighbor Ising model in a $2N\times N$ rectangular box
with a boundary condition inducing the coexistence of the $+$ phase in the bulk
and a layer of $-$ phase along the bottom wall. The presence of an external
magnetic field of intensity $h=\lambda/N$ (for some fixed $\lambda>0$) makes
the layer of $-$ phase unstable. For any $\beta>\beta_{\rm c}$, we prove that,
under a diffusing scaling by $N^{-2/3}$ horizontally and $N^{-1/3}$ vertically,
the interface separating the layer of unstable phase from the bulk phase weakly
converges to an explicit Ferrari-Spohn diffusion.
