Dry Active Matter Exhibits a Self-Organized Cross Sea Phase

The Vicsek modell is known in three different phases: a disordered phase for high noise (or small density), a phase of regularly arranged high density bands with strong polar order that are sourrounded by low density regions with almost no polar order for intermediate noise (or densities), and a (on large scales) spatially homogeneous phase with global polar order for small noise (or high densities). We show that for large systems, there is a fourth phase. It looks like a superposition of bands, tilted in two directions similar to the 'cross sea' phenomenon, sometimes observed in the sea. Here however, the pattern is self-organized and not only a superposition of tilted bands. The density at the crossing points of the pattern is much larger than twice the band density. We show that cross sea phase is separated from the band phase and from the homogeneous polar ordered phase by two discontinuous transitions. We use a local integral of the pair correlation function as an order parameter. Due to the differnt spatial arrangement It can distinguish all four phases. Alternatively, a lattice order parameters leads to similar results.