  A competition of incommensurate symmetries occurs whenever a system is forced
to conform to an ordering that is different from the intrinsically preferred
structure of the system itself. As a model system of such a competition, we
study the rivalry between the triangular ordering of hard disks and the square
symmetry induced by a periodic square substrate. By using density functional
theory as well as Monte Carlo computer simulations, we determine the full phase
behavior for the case of one particle per minimum. We observe a rhombic
preordering structure preceding the hexagonal solid as a direct consequence of
the competing symmetries. Furthermore, the square-rhombic transition is
reentrant with increasing substrate interaction. Our predictions can be
verified in experiments of colloids in laser fields.
