  Combining a semi-classical analysis with exact diagonalizations, we show that
the ground state of the SU(3) Heisenberg model on the square lattice develops
three-sublattice long-range order. This surprising pattern for a bipartite
lattice with only nearest-neighbor interactions is shown to be the consequence
of a subtle quantum order-by-disorder mechanism. By contrast, thermal
fluctuations favor two-sublattice configurations via entropic selection. These
results are shown to extend to the cubic lattice, and experimental implications
for the Mott-insulating states of three-flavor fermionic atoms in optical
lattices are discussed.
