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

TL;DR

This paper investigates the active 4-state Potts model on a square lattice, revealing flocking behavior, a phase diagram, and a novel reorientation transition in phase-separated profiles, supported by hydrodynamic modeling.

Contribution

It introduces a new active Potts model with flocking and phase separation, and uncovers a unique reorientation transition absent in similar models.

Findings

Flocking occurs at high densities and low noise levels.

A phase diagram with coexistence of liquid and gas phases is computed.

A novel reorientation transition from transversal to longitudinal band motion is identified.

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.