Beyond dynamic scaling: Rare events break universality

Surface growth driven by nonmonomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution P(s)∼s^{-τ}. We find that the critical exponents vary continuously with τ, recovering Kardar-Parisi-Zhang behavior only for τ≥3. For τ<3, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale ζ, corresponding to the linear size of the largest cluster, in addition to the usual correlation length ξ. The coexistence of these two relevant scales signals the breakdown of the usual Family-Vicsek scaling. These results point to an interesting phenomenology of surface growth beyond the standard scale-invariant paradigm.