  We study a discrete-space model of active matter with excluded volume.
Particles are restricted to the sites of a triangular lattice, and can assume
one of three orientations. Varying the density and noise intensity, Monte Carlo
simulations reveal a variety of spatial patterns. Ordered states occur in the
form of condensed structures, which (away from the full occupancy limit)
coexist with a low-density vapor. The condensed structures feature low particle
mobility, particularly those that wrap the system via the periodic boundaries.
As the noise intensity is increased, dense structures give way to a disordered
phase. We characterize the parameter values associated with the condensed
phases and perform a detailed study of the order-disorder transition at (1)
full occupation and (2) at a density of 0.1. In the former case, the model
possesses the same symmetry as the three-state Potts model and exhibits a
continuous phase transition, as expected, with critical exponents consistent
with those of the associated Potts model. In the low-density case, the
transition is clearly discontinuous, with strong dependence of the final state
upon the initial configuration, hysteresis,and nonmonotonic dependence of the
Binder cumulant upon noise intensity.
