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

Stability of liquid crystalline phases in the phase-field-crystal model