Polar flocks with discretized directions: the active clock model approaching the Vicsek model

Abstract

We consider the off-lattice two-dimensional $q$-state active clock model (ACM) as a natural discretization of the Vicsek model (VM) describing flocking. The ACM consists of particles able to move in the plane in a discrete set of $q$ equidistant angular directions, as in the active Potts model (APM), with an alignment interaction inspired by the ferromagnetic equilibrium clock model. We find that for a small number of directions, the flocking transition of the ACM has the same phenomenology as the APM, including macrophase separation and reorientation transition. For a larger number of directions, the flocking transition in the ACM becomes equivalent to the one of the VM and displays microphase separation and only transverse bands, i.e. no re-orientation transition. Concomitantly also the transition of the $q\to \infty$ limit of the ACM, the active XY model (AXYM), is in the same universality class as the VM. We also construct a coarse-grained hydrodynamic description for the ACM and AXYM akin to the VM.

18 pages, 12 figures, 1 table, supplementary material merged to the main text

References in corpus (5)

• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• Traffic jams, gliders, and bands in the quest for collective motion
• Flocking with a $q$-fold discrete symmetry: band-to-lane transition in the active Potts model