Dynamic critical phenomena in fractals

Dynamic critical phenomena are investigated, via the spin-flip kinetic Ising model, on two finitely ramified fractals: the Sierpinski gasket (SG) and the Koch curve. We show, using the Kawasaki inequality, that the dynamic critical exponent of the SG satisfies z≥$d_f$, the lower bound forming the conventional value. We also formulate a lower bound for the characteristic decay time. For the Koch curve we show exactly that z=2$d_f$=$d_w$, where $d_w$ is the random-walk dimension.