  We model a system of ultracold fermionic dipolar molecules on a
two-dimensional square lattice. Assuming that the molecules are in their
nondegenerate hyperfine ground state, and that the dipole moment is polarized
perpendicular to the plane (as in the recent experiments on 40K-87Rb
molecules), we approximate these molecules as spinless fermions with long range
repulsive dipolar interactions. We use mean field theory to obtain the
restricted phase diagram as a function of the filling, the strength of
interaction and the temperature. We find a number of ordered density wave
phases in the system, as well as phase separation between these phases. A Monte
Carlo analysis shows that the higher-period phases are usually suppressed in
the exact solution.
