Phases and phase transitions in flocking systems

In this paper, we briefly review some recent theoretical and numerical progress in understanding flocking dynamics. On the theoretical side, a continuum model has been successfully used in explaining the hydrodynamic properties of the flock dynamics. In particular, the long-range ordered state has been shown to be stable even in two dimensions. On the numerical side, study of a discrete model which includes both body force interaction and alignment force reveals a very rich phase diagram. The potential of such models in describing finite flocks is discussed. In the end, we list some unanswered questions and new directions for future studies.