Flocking in the Active Ising Model

The Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at a finite temperature in dimensions two or less in equilibrium systems with short-range interactions. Far from equilibrium, this restriction need not hold, as revealed by the spontaneous flocking of self-propelled particles with polar alignment in two dimensions as in, e.g. the Vicsek model. Most flock phenomenology can be captured by a simpler, discrete-symmetry model known as the Active Ising Model — an active analogue to the equilibrium Ising Model. In this talk, I will present numerical and analytical results which show that the dynamics of the active Ising flock are far richer than previously thought.