Non-reciprocal forces and exceptional phase transitions in metric and topological flocks

The Vicsek model is a cornerstone in the field of active matter and has been the basis for many other models of flocking involving alignment rules based on the mean orientation of neighboring particles. Yet, the implications of an implicit violation of Newton's third law in the alignment rule remains poorly understood. Here we show that in the absence of this microscopic non-reciprocity an exceptional phase transition is predicted at low noise strength within the Toner-Tu framework of polar aligning matter; we demonstrate this transition via large-scale numerical simulations. When microscopic non-reciprocal forces found in more common models of flocking are present, we show that they coarse-grain into additional hydrodynamic terms which non-reciprocally couple the density and momentum fields. This leads to a highly ordered clustered phase in metric models and restore the homogeneous flocking phase in topological models.