Abstract
It is proven by Peierls' argument in connection with reflection positivity that the lattice gas on the FCC lattice with nearest-neighbour repulsion (with interaction energy a) exists in an ordered state at low enough temperature provided the chemical potential, mu , satisfies 0< mu <4a, 4a< mu <8a or 8a< mu <12a. This result immediately carries over to the antiferromagnetic Ising model and the lattice gas with nearest-neighbour exclusion on the FCC lattice, both of which will also exist in an ordered state under suitable circumstances. In particular, the existence of a phase transition at zero magnetic field is confirmed.