  We explore the physics of highly frustrated magnets in confined geometries,
focusing on the Coulomb phase of pyrochlore spin ices. As a specific example,
we investigate thin films of nearest-neighbor spin ice, using a combination of
analytic large-N techniques and Monte Carlo simulations. In the simplest film
geometry, with surfaces perpendicular to the [001] crystallographic direction,
we observe pinch points in the spin-spin correlations characteristic of a
two-dimensional Coulomb phase. We then consider the consequences of crystal
symmetry breaking on the surfaces of the film through the inclusion of orphan
bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is
destroyed by the presence of fluctuating surface magnetic charges, leading to a
classical Z_2 spin liquid. Building on this understanding, we discuss other
film geometries with surfaces perpendicular to the [110] or the [111]
direction. We generically predict the appearance of surface magnetic charges
and discuss their implications for the physics of such films, including the
possibility of an unusual Z_3 classical spin liquid. Finally, we comment on
open questions and promising avenues for future research.
