SCALING OF THE POINT-POINT CORRELATION FUNCTION OF DLA

Abstract

The scaling of the point-point correlation function of DLA has shown itself to be more complex and challenging than had at first been imagined. This paper determines from the results of previous studies that a more general scaling rule must be applied, at least robust enough to allow different moments of the point-point correlation function to scale non-trivially, and for the scale length to scale non-trivially. In this sense, it is seen that the scaling problem is analogous to that of multifractal scaling. The authors present a group-theoretic derivation of the most general scaling transformations possible, and show that it is adequately robust to explain the non-trivial scaling observed in the moments of the point-point correlation function.