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We study the homogeneous nearest-neighbor Ising ferromagnet on the right halfplane with a Dobrushin type boundary condition --- say plus on the top part ofthe boundary and minus on the bottom. For sufficiently low temperature $T$, wecompletely 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 regionswhere 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, thereis at least one pure state for each $\theta$.

A continuum of pure states in the Ising model on a halfplane