We study the active 4-state Potts model (APM) on the square lattice in which active particles have four internal states corresponding to the four directions of motion. A local alignment rule inspired by the ferromagnetic 4-state Potts model and self-propulsion via biased diffusion according to the internal particle states leads to flocking at high densities and low noise. We compute the phase diagram of the APM and explore the flocking dynamics in the region, in which the high-density (liquid) phase coexists with the low-density (gas) phase and forms a fluctuating band of coherently moving particles. As a function of the particle self-propulsion velocity, a novel reorientation transition of the phase-separated profiles from transversal to longitudinal band motion is revealed, which is absent in the Vicsek model and the active Ising model. We further construct a coarse-grained hydrodynamic description of the model which validates the results for the microscopic model.

中文翻译：

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四态有源Potts模型中的植绒和重新定向过渡

我们在正方形晶格上研究了主动四态Potts模型（APM），其中主动粒子具有与四个运动方向相对应的四个内部状态。受铁磁4态Potts模型启发的局部对准规则以及根据内部粒子状态通过有偏扩散进行的自推进会导致在高密度和低噪声时发生植绒。我们计算了APM的相图，并探索了该区域的植绒动力学，在该区域中高密度（液相）与低密度（气相）共存，并形成了相干运动的粒子的波动带。作为粒子自推进速度的函数，揭示了相分离轮廓从横向运动到纵向带运动的新的重新定向转变，这在Vicsek模型和活动Ising模型中是不存在的。