Flocking dynamics with voter-like interactions

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a 2D space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter phi, until complete order phi = 1.0 is reached (polar consensus). We find that phi increases as t(1/2) for short times and approaches 1.0 exponentially fast for longer times. Also, the mean time to consensus tau varies non-monotonically with the density of particles rho reaching a minimum at some intermediate density rho(min). At rho(min), the mean consensus time scales with the system size N as tau(min) similar to N-0.765, and thus the consensus is faster than in the case of all-to-all interactions (large rho) where tau = 2N. We show that the fast consensus, also observed at intermediate and high densities, is a consequence of the segregation of the system into clusters of equally-oriented particles which breaks the balance of transitions between directional states in well mixed systems.