Breakdown of multifractal behavior in diffusion-limited aggregates

Analytic arguments are presented, concerning the phase transition to nonmultifractal behavior of the qth moment, Mq, of growth probabilities in diffusion-limited aggregation, found numerically by Lee and Stanley. Assuming the existence of exponentially small growth probabilities, for a single growing aggregate, we find a transition at q=0. For aggregates of size L, this transition splits into two at q0(L)<qc(L)<0. Quantitative analysis of q0(L) yields information on the tail of the growth probability distribution. Averaging Mq over all aggregates may yield a finite q0.