Three-state active lattice gas: A discrete Vicsek-like model with excluded volume

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 (i) full occupation and (ii) 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 a strong dependence of the final state upon the initial configuration, hysteresis, and nonmonotonic dependence of the Binder cumulant upon noise intensity.