Non-reciprocal interactions in flocking models

Active matter is a field within out-of-equilibrium statistical physics that studies systems at the microscopic scale capable of converting ambient energy into self-propulsion or other forms of mechanical motion. The Vicsek model (VM), which describes the transition to collective motion in self-propelled particles, serves as a paradigmatic example in this discipline. Known for its simplicity and numerical tractability, the VM effectively captures the onset of flocking behavior. While fundamental forces must obey Newton’s action-reaction principle, effective descriptions of active matter systems often involve reciprocity-breaking interactions, especially at the mesoscopic level, where such interactions may be more the rule than the exception. A striking consequence of non-reciprocal (NR) interactions in two-species systems is the emergence of chiral phases. This raises the question of whether chiral phases, or other forms of chirality, can emerge in one-species NR active models. Prior work on active smectics introduced variants of the Vicsek model incorporating pairwise non-reciprocal repulsion and noted the spontaneous emergence of global rotation. In this study, a numerical investigation of chirality-breaking mechanisms in the non-reciprocal Vicsek model is presented, aiming to explore the potential role of NR interactions in the emergence of chiral phases. To this end, a smectic order parameter is introduced as a numerical tool to analyze rotational dynamics. The dependence on non-reciprocal repulsion strength is then quantified through an exponential fit of the angular velocity autocorrelation function.