  We investigate the possibility to control the symmetry of ordered states in
phase-field crystal models by tuning nonlinear resonances. In two dimensions,
we find that a state of square symmetry as well as coexistence between squares
and hexagons can be easily obtained. In contrast, it is delicate to obtain
coexistence of squares and liquid. We develop a general method for constructing
free energy functionals that exhibit solid-liquid coexistence with desired
crystal symmetries. As an example, we develop a free energy functional for
square-liquid coexistence in two dimensions. A systematic analysis for
determining the parameters of the necessary nonlinear terms is provided. The
implications of our findings for simulations of materials with simple cubic
symmetry are discussed.
