Breakdown of multifractal behavior in diffusion-limited aggregates

Analytic arguments are presented, concerning the ‘‘phase transition’’ to nonmultifractal behavior of the qth moment, $M_q$, 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 $q_0$(L)<$q_c$(L)<0. Quantitative analysis of $q_0$(L) yields information on the tail of the growth probability distribution. Averaging $M_q$ over all aggregates may yield a finite $q_0$.