Phase Transition in the Multifractal Spectrum of Diffusion-Limited Aggregation

Based on a novel "exact enumeration" approach, we find evidence suggesting the existence of a phase transition in the multifractal spectrum of diffusion-limited aggregation. Above a critical point βc, the moment expansion shows an infinite hierarchy of phases, while below βc we find a single phase. At βc we find fluctuations of all energy scales and singular behavior of the energy and specific heat. We also find that the maximum energy scales with system size L as Eₘₐₓ(L)∝L²InL. Consequently, for β<βc the partition function does not scale with L, which implies that the conventional moment expansion must break down.