  Common density-matrix functionals, the M\"uller and the power functional,
have been benchmarked for the half-filled Hubbard dimer, which allows to model
the bond dissociation problem and the transition from the weakly to the
strongly correlated limit. Unbiased numerical calculations are combined with
analytical results. Despite the well known successes of the M\"uller
functional, the ground state is degenerate with a one-dimensional manifold of
ferromagnetic solutions. The resulting infinite magnetic susceptibility
indicates another qualitative flaw of M\"uller's functional. The derivative
discontinuity with respect to particle number is not present indicating an
incorrect metal-like behavior. The power functional actually favors the
ferromagnetic state for weak interaction. Analogous to the Hartree-Fock
approximation, the power functional undergoes a transition beyond a critical
interaction strength, in this case however, to a non-collinear
antiferromagnetic state.
