  We use the dual boson approach to reveal the phase diagram of the
Fermi-Hubbard model with long-range dipole-dipole interactions. By using a
large-scale finite-temperature calculation on a $64 \times 64$ square lattice
we demonstrate the existence of a novel phase, possessing an `ultralong-range'
order. The fingerprint of this phase -- the density correlation function --
features a non-trivial behavior on a scale of tens of the lattice sites. We
study the properties and the stability of the ultralong-range ordered phase,
and show that it is accessible in modern experiments with ultracold polar
molecules and magnetic atoms.
