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The disordered ferromagnet is a disordered version of the ferromagnetic Isingmodel in which the coupling constants are non-negative quenched random. Aground configuration is an infinite-volume configuration whose energy cannot bereduced by finite modifications. It is a long-standing challenge to ascertainwhether the disordered ferromagnet on the $\mathbb{Z}^D$ lattice admitsnon-constant ground configurations. We answer this affirmatively in dimensions$D\ge 4$, when the coupling constants are sampled independently from asufficiently concentrated distribution. The obtained ground configurations arefurther 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 byDobrushin boundary conditions is localized, and converges to an infinite-volumeinterface. This may be expressed in purely combinatorial terms, as a result onthe fluctuations of certain minimal cutsets in the lattice $\mathbb{Z}^D$endowed with independent edge capacities.

Non-constant ground configurations in the disordered ferromagnet