Scaling of Kinetically Growing Clusters

Abstract

A model describing the process of cluster growth by aggregation of clusters is introduced and investigated with the Monte Carlo method. It is found that the clusters are scale invariant. The fractal dimension of this new class of kinetic critical behavior is $D={\ensuremath{\nu}}^{\ensuremath{-}1}=1.38\ifmmode\pm\else\textpm\fi{}0.06$ in $d=2$ dimensions as determined by the radii of gyration and the density correlations of the aggregates. The process is compared with other types of kinetic and equilibrium critical phenomena.