  Ensembles of driven or motile bodies moving along opposite directions are
generically reported to self-organize into strongly anisotropic lanes. Here,
building on a minimal model of self-propelled bodies targeting opposite
directions, we first evidence a critical phase transition between a mingled
state and a phase-separated lane state specific to active particles. We then
demonstrate that the mingled state displays algebraic structural correlations
also found in driven binary mixtures. Finally, constructing a hydrodynamic
theory, we single out the physical mechanisms responsible for these universal
long-range correlations typical of ensembles of oppositely moving bodies.
