  We construct a density functional for the lattice gas / Ising model on square
and cubic lattices based on lattice fundamental measure theory. In order to
treat the nearest-neighbor attractions between the lattice gas particles, the
model is mapped to a multicomponent model of hard particles with additional
lattice polymers where effective attractions between particles arise from the
depletion effect. The lattice polymers are further treated via the introduction
of polymer clusters (labelled by the numbers of polymer they contain) such that
the model becomes a multicomponent model of particles and polymer clusters with
nonadditive hard interactions. The density functional for this nonadditive hard
model is constructed with lattice fundamental measure theory. The resulting
bulk phase diagram recovers the Bethe-Peierls approximation and planar
interface tensions show a considerable improvement compared to the standard
mean-field functional and are close to simulation results in three dimensions.
We demonstrate the existence of planar interface solutions at chemical
potentials away from coexistence when the equimolar interface position is
constrained to arbitrary real values.
