Mean-field theory of the morphology transition in stochastic diffusion-limited growth

We propose a mean-field model for describing the averaged properties of a class of stochastic diffusion-limited growth systems. We then show that this model exhibits a morphology transition from a dense-branching structure with a convex envelope to a dendritic one with an overall concave morphology. We also construct an order parameter that describes the transition quantitatively. The transition is shown to be continuous, which can be verified by noting the nonexistence of any hysteresis.