Tiago Venzel Rosembach

arXiv2026

Mean-Field Theory for the Three-State Active Lattice Gas Model

We develop a mean-field description including spatial structure for a simplified version of the three-state active matter model studied by Venzel et al. (Phys. Rev. E 110, 014109 (2024)). The resulting triangular lattice of coupled nonlinear differential equations are integrated numerically using a fourth-order Runge-Kutta scheme. Starting from various ordered initial configurations, we probe the stability of the corresponding stationary states, revealing the presence of various high-density ordered structures in the density(\r{ho})-noise(η) plane. The results are compared with Monte Carlo simulations of the simplified model, yielding, in certain cases, unexpected transitions between ordered configuration types.

cond-mat.stat-mech↗

arXiv2024

Three-state active lattice gas: a discrete Vicseklike 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 (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.

cond-mat.stat-mech↗