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

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

1997-06-04

arxiv.org/abs/physics/9706008v2

Phys. Rev. Lett. 78, 5018-5021 (1997)

Physics

Biological Physics

4 pages, 4 figures, final version as published

Scientific paper

10.1103/PhysRevLett.78.5018

A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local 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 predictions for the two critical exponents describing the phase transition as a function of sensitivity and density are obtained analytically.

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