Fractality of DLA in an arbitrary Euclidean dimension beyond the on-lattice and mean-field approximations

Abstract

The derivation of a consistent analytical description for the fractality of the paradigmatic diffusion-limited aggregation (DLA) model, valid beyond the on-lattice and mean-field approximations in any embedding space, has been lengthy pursuit issue in out-of-equilibrium growth research. Here, by unifying previous renormalization-group and mean-field proposals, we provide such general solution to the scaling of the DLA cluster and to its harmonic measure as well. This result is in excellent agreement with available and reliable results for the fractal dimensions of DLA reported over the years, and in particular, it consistently establishes \(D=1+1/\sqrt{2}\approx 1.707\), for two-dimensions.