  The quantum dimer model, relevant for short-range resonant valence bond
physics, is rigorously shown to have long range order in a crystalline phase in
the attractive case at low temperature and not too large flipping term. This
term flips horizontal dimer pairs to vertical pairs (and vice versa) and is
responsible for the word `quantum' in the title. In addition to the dimers,
monomers are also allowed. The mathematical method used is `reflection
positivity'. The model and proof can easily be generalized to dimers or
plaquettes in 3-dimensions.
