Phase Transitions of Ultradiffusion Model on Vicsek Snowflakes Fractal

Through an exact real space renormaligation group approach, we analysed the ultradiffusion with a hierarchical pattern of hopping rates defined on Vicsek snowflackes fractal. The transition from anomalous to normal diffusion is shown to occur in the arbitrary n-dimension (n-D) case. In the presence of external field, we find another unusual transition which is essentially different from the one for biased ultradiffusion of 1-D multifurcating hierarchical system.