Probability scaling for diffusion-limited aggregation in higher dimensions
- 1 January 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 33 (1) , 786-788
- https://doi.org/10.1103/physreva.33.786
Abstract
We extend to dimensions d≥2 our scaling treatment of the perimeter occupancy probabilities for diffusion-limited aggregation (DLA) clusters grown on lattices. We obtain an analytic relation for the Hausdorff dimension D. We find no upper critical dimension for DLA, although D→d-1 for large d. Our theoretical values for D are fully consistent with Meakin’s Cartesian lattice simulations for 2≤d≤6. We have studied the nonuniversality (lattice dependence) of D by shearing the Cartesian lattices. For maximal shear, D=d-1 (mean field) for d≥3.Keywords
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