Critical dynamics of the kinetic Ising model with triplet interaction on Sierpin´ski-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 Sierpin´ski-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/ν, where ν is the static correlation exponent and independent of the member of the fractal family. However, for energylike perturbation, z_E=2/ν and z_E is independent of the member of the fractal family. In particular, for the two-dimensional Sierpin´ski gasket, z_E=z_M=2/ν=1/ν+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.