Critical dynamics of the kinetic Ising model on the fractal Koch curves

The critical slowing down of the kinetic Glauber-Ising model on different fractal geometries with quasilinear lattices is studied. The classes of fractals which are examined are the nonbranching Koch curves and the branching Koch curves. The relaxation of two different perturbations from equilibrium is examined. The dynamic critical exponent is calculated for these lattices using an exact renormalization-group transformation. The value z=1/ν+$D_f$ is found for both fractals.