  The phase-field-crystal model for liquid crystals is solved numerically in
two spatial dimensions. This model is formulated with three position-dependent
order parameters, namely the reduced translational density, the local nematic
order parameter, and the mean local direction of the orientations. The
equilibrium free-energy functional involves local powers of the order
parameters up to fourth order, gradients of the order parameters up to fourth
order, and different couplings between the order parameters. The stable phases
of the equilibrium free-energy functional are calculated for various coupling
parameters. Among the stable liquid-crystalline states are the isotropic,
nematic, columnar, smectic A, and plastic crystalline phases. The plastic
crystals can have triangular, square, and honeycomb lattices and exhibit
orientational patterns with a complex topology involving a sublattice with
topological defects. Phase diagrams were obtained by numerical minimization of
the free-energy functional. Their main features are qualitatively in line with
much simpler one-mode approximations for the order parameters.
