  The short-time dynamic evolution of an Ising model embedded in an infinitely
ramified fractal structure with noninteger Hausdorff dimension was studied
using Monte Carlo simulations. Completely ordered and disordered spin
configurations were used as initial states for the dynamic simulations. In both
cases, the evolution of the physical observables follows a power-law behavior.
Based on this fact, the complete set of critical exponents characteristic of a
second-order phase transition was evaluated. Also, the dynamic exponent $\theta
$ of the critical initial increase in magnetization, as well as the critical
temperature, were computed. The exponent $\theta $ exhibits a weak dependence
on the initial (small) magnetization. On the other hand, the dynamic exponent
$z$ shows a systematic decrease when the segmentation step is increased, i.e.,
when the system size becomes larger. Our results suggest that the effective
noninteger dimension for the second-order phase transition is noticeably
smaller than the Hausdorff dimension. Even when the behavior of the
magnetization (in the case of the ordered initial state) and the
autocorrelation (in the case of the disordered initial state) with time are
very well fitted by power laws, the precision of our simulations allows us to
detect the presence of a soft oscillation of the same type in both magnitudes
that we attribute to the topological details of the generating cell at any
scale.
