Abstract
By the exact time-dependent renormalization-group method, the critical dynamics of the kinetic Ising model on a family of regular fractal models is studied for the diffusion-limited-aggregation (DLA) model cluster. The scaling law of the dynamics exponent, Z=Df+2/ν, is found and it is shown that ν (the static correlation exponent) is independent of the choice of regular DLA clusters. The dynamics exponent Z=Df+2/ν is therefore proposed for a random DLA cluster.