CRITICAL-DYNAMICS OF THE KINETIC ISING-MODEL WITH TRIPLET INTERACTION ON SIERPINSKI-GASKET-TYPE FRACTALS

By use of the time-dependent renormalization-group method, the critical dynamics of the kinetic triplet-interaction Ising model on a family of Sierpinski-gasket-type fractals is studied. We find that for magneticlike perturbation the scaling law of the dynamic exponent has the form z(M) = d(f) + 3/v, where v is the static correlation exponent and independent of the member of the fractal family. However, for energylike perturbation, z(E) = 2/v and z(E) is independent of the member of the fractal family. In particular, for the two-dimensional Sierpinski gasket, z(E) = z(M) = 2/v = 1/v + d(f) is different from the result, z = 1 + d(f), of the two-spin-interaction Ising model due to Achiam. This implies that the dynamic universality hypothesis is violated.