Matéria ativa em rede: um modelo do tipo Vicsek com volume excluído

Abstract

In recent decades, the study of collective motion has garnered significant interest from the scientific community. The application of statistical mechanics techniques has led to a better understanding of these types of systems, known as active matter. Through computational models, combined with nonequilibrium phase transition concepts, common characteristics, that are independent of scale, have been established for active matter. In this context, the model proposed by Vicsek et al. (1995), despite its simplicity, serves as a starting point for various generalizations and variations that have been applied to a wide range of different problems. Aiming to understand the applicability limits of the Vicsek universality class, we proposed a model that follows the basic rules of the original model, implemented in an active matter system on a triangular lattice, where the particles can only assume three velocities and the sites can only be occupied by a single particle (exclusion volume). Monte Carlo simulations revealed that, varying the density and noise intensity, our model exhibits a variety of spatial patterns in the stationary states. Ordered states occur in the form of condensed structures, which, except in a fully occupied lattice, coexist with a low-density vapor and eventually disband for sufficiently large noise. Additionally, we use the order parameter to conduct a detailed study of the ordereddisordered transition for (i) a density equal to 0.1 and (ii) a fully occupied lattice. In the first case, we found that the transition is discontinuous, with hysteresis curves, nonmonotonic behavior for the Binder cumulant, among others. In the second case, we observed a continuous phase transition, with critical exponents β/ν = 0.138(3) and γ/ν = 1.70(2), consistent with those of the three-state Potts model.