The phase-field crystal (PFC) model allows for the resolution of atomic-scale structures on diffusive time scales. It is based on an approximation of the two-particle direct correlation function in the free energy, which provides the symmetry of the lattice structure. Various approaches have been proposed to model common lattices. We here only focus on two-dimensional crystals, review the different approaches and demonstrate that one, which is based on affine linear deformations, violates rotational invariance. The consequences of this physical inconsistency are shown numerically using a pseudospectral algorithm for the higher order equations.

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