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

We study a system of self-propelled particles whose alignment with neighbors depends on the degree of local alignment. We show that such a local conformity interaction naturally yields a Vicsek-type model with pairwise and three-body interactions. Through numerical and approximate theoretical investigation of its deterministic and stochastic collective dynamics, we identify a novel bidirectionally ordered phase in which the particles move in opposite directions. Moreover, both continuous and discontinuous order-disorder transitions are observed, suggesting that the system belongs to a different universality class from previous models.