  In this work we have studied the dynamic scaling behavior of two scaling
functions and we have shown that scaling functions obey the dynamic finite size
scaling rules. Dynamic finite size scaling of scaling functions opens
possibilities for a wide range of applications. As an application we have
calculated the dynamic critical exponent ($z$) of Wolff's cluster algorithm for
2-, 3- and 4-dimensional Ising models. Configurations with vanishing initial
magnetization are chosen in order to avoid complications due to initial
magnetization. The observed dynamic finite size scaling behavior during early
stages of the Monte Carlo simulation yields $z$ for Wolff's cluster algorithm
for 2-, 3- and 4-dimensional Ising models with vanishing values which are
consistent with the values obtained from the autocorrelations. Especially, the
vanishing dynamic critical exponent we obtained for $d=3$ implies that the
Wolff algorithm is more efficient in eliminating critical slowing down in Monte
Carlo simulations than previously reported.
