  We study the atomistic-to-continuum limit of a class of energy functionals
for crystalline materials via Gamma-convergence. We consider energy densities
that may depend on interactions between all points of the lattice and we give
conditions that ensure compactness and integral-representation of the continuum
limit on the space of special functions of bounded variation. This abstract
result is complemented by a homogenization theorem, where we provide sufficient
conditions on the energy densities under which bulk- and surface contributions
decouple in the limit. The results are applied to long-range and multi-body
interactions in the setting of weak-membrane energies.
