Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion

A cellular automaton model is presented for random walkers with biologically motivated interactions favoring loral alignment and leading To collective motion or swarming behavior. The degree of alignment-is controlled by a sensitivity parameter, and a dynamical phase transition exhibiting spontaneous breaking of rotational symmetry occurs at a critical parameter value. The model is analyzed using nonequilibrium mean-field theory: Dispersion relations for the critical modes are derived, and a phase diagram is constructed. Mean-field prediction for the two critical exponents describing the phase transition as a function of sensitivity and density are obtained analytically.