  We consider two species of self-propelled point particles: A-particles and
B-particles. The orientations between nearby particles are subject to pair
interactions of different strength for A-A-, A-B-(=B-A-) and B-B-interactions,
respectively. Even if all interactions involved are repelling, that is, if they
locally favor anti-alignment between each pair of particles, we find global
polar order of both A-particles and B-particles We find qualitative agreement
between agent-based simulations and mean field theory. Beyond mean field, we
develop a Boltzmann-scattering theory based on one-sided molecular chaos that
yields excellent quantitative agreement with simulations for dilute systems.
For large systems, we find, depending on parameters, either
micro-phase-separation or static patterns with either patches or stripes that
carry different polarization orientations.
