For the Kuramoto model, a minimum of the Lyapunov function corresponds to a ground state of a system with frustration: the interaction between the oscillators, XY spins, is ferromagnetic, whereas the
random frequencies induce random fields which try to break the ferromagnetic order, i.e., global phase locking. Special attention is given to discrete distribution functions. We argue that in this case a perfect locking on each of the sublattices which correspond to the frequencies results, but that a partial locking of some but not all sublattices is not to be expected.