We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these objects are not present. A statistically-homogeneous ordered phase is then observed, which is characterized by anomalously-strong density fluctuations, superdiffusion, and strong intermittency.

We study, in two space dimensions, the large-scale properties of collections of constant-speed polar point particles interacting locally by nematic alignment in the presence of noise. This minimal approach to self-propelled rods allows one to deal with large numbers of particles, revealing a phenomenology previously unseen in more complicated models, and moreover distinctively different from both that of the purely polar case (e.g. the Vicsek model) and of active nematics.PACS numbers: 05.65.+b, 87.18.Hf, 87.18.Gh Collective motion is an ubiquitous phenomenon observable at all scales, in natural systems [1] as well as human societies [2]. The mechanisms at its origin can be remarkably varied. For instance, they may involve the hydrodynamic interactions mediated by the fluid in which bacteria swim [3], the long-range chemical signaling driving the formation and organization of aggregation centers of Dictyostelium discoideum amoeba cells [4], or the local cannibalistic interactions between marching locusts [5]. In spite of this diversity, one may search for possible universal features of collective motion, a context in which the study of "minimal" models is a crucial step. Recently, the investigation of the simplest cases, where the problem is reduced to the competition between a local aligning interaction and some noise, has revealed a wealth of unexpected collective properties. For example, constant speed, self-propelled, polar point particles with ferromagnetic interactions subjected to noise (as in the Vicsek model [6]) can form a collectively moving fluctuating phase with long-range polar order even in two spatial dimensions [7], with striking properties such as spontaneous segregation into ordered solitary bands moving in a sparse, disordered sea, or anomalous ("giant") density fluctuations [8]. In contrast, active apolar particles with nematic interactions only exhibit quasi-long-range nematic order in two dimensions with segregation taking the form of a single, strongly-fluctuating, dense structure with longitudinal order and even stronger density fluctuations than in the polar-ferromagnetic case [9,10,11].Noting that these differences reflect those in the local symmetry of particles and their interactions, a third situation can be defined, intermediate between the polar ferromagnetic model and the apolar nematic one, that of self-propelled polar particles aligning nematically [12]. Such a mechanism is typically induced by volume exclusion interactions, when elongated particles colliding almost head-on slide past each other, as illustrated schematically in Fig. 1. Thus, self-propelled polar point particles with apolar interactions can be conceived as a minimal model for self-propelled rods interacting by inelastic collisions [13,14,15]. Other relevant situations can be found in a biological context, such as gliding myxobacteria moving on a substrate [16], or microtubules driven by molecular motors grafted on a surface [17].In this Letter, we study collections of constant-speed polar point particles inte...