  We study dynamic self-organisation and order-disorder transitions in a
two-dimensional system of self-propelled particles. Our model is a variation of
the Vicsek model, where particles align the motion to their neighbours but
repel each other at short distances. We use computer simulations to measure the
orientational order parameter for particle velocities as a function of
intensity of internal noise or particle density. We show that in addition to
the transition to an ordered state on increasing the particle density, as
reported previously, there exists a transition into a disordered phase at the
higher densities, which can be attributed to the destructive action of the
repulsions. We demonstrate that the transition into the ordered phase is
accompanied by the onset of algebraic behaviour of the two-point velocity
correlation function and by a non-monotonous variation of the velocity
relaxation time. The critical exponent for the decay of the velocity
correlation function in the ordered phase depends on particle concentration at
low densities but assumes a universal value in more dense systems.
