  We study the active 4-state Potts model (APM) on the square lattice in which
active particles have four internal states corresponding to the four directions
of motion. A local alignment rule inspired by the ferromagnetic 4-state Potts
model and self-propulsion via biased diffusion according to the internal
particle states leads to flocking at high densities and low noise. We compute
the phase diagram of the APM and explore the flocking dynamics in the region,
in which the high-density (liquid) phase coexists with the low-density (gas)
phase and forms a fluctuating band of coherently moving particles. As a
function of the particle self-propulsion velocity, a novel reorientation
transition of the phase-separated profiles from transversal to longitudinal
band motion is revealed, which is absent in the Vicsek model and the active
Ising model. We further construct a coarse-grained hydrodynamic description of
the model which validates the results for the microscopic model.
