  We consider the two-dimensional Ising model with long-range pair interactions
of the form $J_{xy}\sim|x-y|^{-\alpha}$ with $\alpha>2$, mostly when $J_{xy}
\geq 0$. We show that Dobrushin states (i.e. extremal non-translation-invariant
Gibbs states selected by mixed $\pm$-boundary conditions) do not exist. We
discuss possible extensions of this result in the direction of the
Aizenman-Higuchi theorem, or concerning fluctuations of interfaces. We also
mention the existence of rigid interfaces in two long-range anisotropic
contexts.
