  We study the homogeneous nearest-neighbor Ising ferromagnet on the right half
plane with a Dobrushin type boundary condition --- say plus on the top part of
the boundary and minus on the bottom. For sufficiently low temperature $T$, we
completely characterize the pure (i.e., extremal) Gibbs states, as follows.
There is exactly one for each angle $\theta\in\lbrack-\pi/2,+\pi/2]$; here
$\theta$ specifies the asymptotic angle of the interface separating regions
where the spin configuration looks like that of the plus (respectively, minus)
full-plane state. Some of these conclusions are extended all the way to
$T=T_{c}$ by developing new Ising exact solution result -- in particular, there
is at least one pure state for each $\theta$.
