Laboratoire de Physique Théorique
Toulouse - UMR 5152

We study the q-state active Potts model (APM) on a two-dimensional lattice in which active particles have q internal states corresponding to the q directions of motion. A local alignment rule inspired by the ferromagnetic q-state Potts model and self-propulsion via biased diffusion according to the internal particle states leads to a collective motion at high densities and low noise. We formulate a coarse-grained hydrodynamic theory with which we compute the phase diagram of the APM and explore the flocking dynamics in the region, in which the high-density (polar 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 found, which is absent in the Vicsek model [1] and the active Ising model [2]. The origin of this reorientation transition is revealed by a stability analysis : for large velocities the transverse diffusion constant approaches zero and then stabilizes longitudinal band motion. Computer simulations corroborate the analytical predictions of the flocking and reorientation transitions and validate the phase diagrams of the APM [3].

[1] T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).

[2] A. P. Solon and J. Tailleur, Phys. Rev. Lett. 111, 078101 (2013) ; Phys. Rev. E 92, 042119 (2015).

[3] S. Chatterjee, M. Mangeat, R. Paul, and H. Rieger, EPL 130, 66001 (2020) ; M. Mangeat, S. Chatterjee, R. Paul, and H. Rieger, Phys. Rev. E 102, 042601 (2020).