Collective dynamics of higher-order Vicsek model emerging from local conformity interactions

The Vicsek model is the paradigmatic framework for collective motion in systems of self-propelled particles. In its continuous-time formulation and most of its extensions, alignment arises from pairwise interactions among neighboring particles. In this work, we consider a model in which each particle assigns weights to its neighbors according to their alignment with the local consensus. This simple mechanism naturally yields a Vicsek-type model with pairwise and higher-order (i.e., nonpairwise) interactions. We analyze its collective dynamics through numerical simulations and approximate theory in the absence and presence of noise. The higher-order interactions generate a novel bidirectionally ordered phase, in which particles self-organize into oppositely moving groups. Moreover, we show that, depending on the relative strength of the pairwise and three-body interactions, the order-disorder transition can be either continuous or abrupt.