  The disordered ferromagnet is a disordered version of the ferromagnetic Ising
model in which the coupling constants are non-negative quenched random. A
ground configuration is an infinite-volume configuration whose energy cannot be
reduced by finite modifications. It is a long-standing challenge to ascertain
whether the disordered ferromagnet on the $\mathbb{Z}^D$ lattice admits
non-constant ground configurations. We answer this affirmatively in dimensions
$D\ge 4$, when the coupling constants are sampled independently from a
sufficiently concentrated distribution. The obtained ground configurations are
further shown to be translation-covariant with respect to $\mathbb{Z}^{D-1}$
translations of the disorder.
  Our result is proved by showing that the finite-volume interface formed by
Dobrushin boundary conditions is localized, and converges to an infinite-volume
interface. This may be expressed in purely combinatorial terms, as a result on
the fluctuations of certain minimal cutsets in the lattice $\mathbb{Z}^D$
endowed with independent edge capacities.
