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We study a discrete-space model of active matter with excluded volume.Particles are restricted to the sites of a triangular lattice, and can assumeone of three orientations. Varying the density and noise intensity, Monte Carlosimulations reveal a variety of spatial patterns. Ordered states occur in theform of condensed structures, which (away from the full occupancy limit)coexist with a low-density vapor. The condensed structures feature low particlemobility, particularly those that wrap the system via the periodic boundaries.As the noise intensity is increased, dense structures give way to a disorderedphase. We characterize the parameter values associated with the condensedphases 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 modelpossesses the same symmetry as the three-state Potts model and exhibits acontinuous phase transition, as expected, with critical exponents consistentwith those of the associated Potts model. In the low-density case, thetransition is clearly discontinuous, with strong dependence of the final stateupon the initial configuration, hysteresis,and nonmonotonic dependence of theBinder cumulant upon noise intensity.

Three-state active lattice gas: a discrete Vicseklike model with excluded volume