Vicsek model

The Vicsek model is a simple model of active matter, such as a swarm of fish or birds. In this model the particles move at constant velocity and tend to align their motion with their neightbors. At each time step their direction are randomly changed by a small amount.

The noise is given in radians and represent the angle in which the noise can be choosen from, as illustrated on the right. The density is given in particles per area, with the area given in unit of the interaction radius.

Like the Ising model, the Vicsek model display a phase transition from an ordered phase, where all particles move in the same direction, to a disordered phase, where all particles move in random directions. This phase transition occurs as the density decreases (or the noise increases), and can be studied through the polarization, the average of the velocities of each particle.