Flocking and reorientation transition in the 4-state active Potts model

¹ Indian Association for the Cultivation of Science - Kolkata 700032, India
² Center for Biophysics & Department for Theoretical Physics, Saarland University - D-66123 Saarbrücken, Germany

^(a) sspsc5@iacs.res.in
^(b) mangeat@lusi.uni-sb.de
^(c) ssprp@iacs.res.in
^(d) h.rieger@mx.uni-saarland.de

Received: 28 February 2020
Accepted: 22 June 2020

Abstract

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.