  Directed manifolds (domain walls, interfaces, vortex lines) in a deformable
medium can exist in a correlated state in which the manifold is self-localized
by its own strain field. Depending on the temperature, manifold/medium
dimensionalities, and the strength of the coupling with the medium, the degree
of localization of the ground state can vary both continuously and
discontinuously; there can be phase transitions from self- localized to the
free-manifold state.
