  We study populations of oscillators, all-to-all coupled by means of quenched
disordered phase shifts. While there is no traditional synchronization
transition with a nonvanishing Kuramoto order parameter, the system
demonstrates a specific order as the coupling strength increases. This order is
characterized by partial phase locking, which is put into evidence by the
introduced correlation order parameter and via frequency entrainment.
Simulations with phase oscillators, Stuart-Landau oscillators, and chaotic
Roessler oscillators demonstrate similar scaling of the correlation order
parameter with the coupling and the system size and also similar behavior of
the frequencies with maximal entrainment at some finite coupling.
