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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 analignment interaction inspired by the ferromagnetic equilibrium clock model. Wefind that for a small number of directions, the flocking transition of the ACMhas the same phenomenology as the APM, including macrophase separation andreorientation transition. For a larger number of directions, the flockingtransition in the ACM becomes equivalent to the one of the VM and displaysmicrophase separation and only transverse bands, i.e. no re-orientationtransition. Concomitantly also the transition of the $q\to\infty$ limit of theACM, 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 andAXYM akin to the VM.

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