directions. In addition, we expect the remarkable feature of unique scaling functions for different values of $p$ to be peculiar to the one-dimensional case. Considering the function $G(r,t)$, for instance, the scaling function describes the spatial distribution of domains and it is quite evident that in $d>1$ this depends on $p$. Taking the case $d=2$, for simplicity, one has the usual bicontinuous domain structure of domains and interfaces for $p=2$, while for $p>2$ there is a different pattern with interfaces and vortices [@Kaski83]. However, in the one dimensional case interfaces are point-like objects for all values of $p$ and one does not expect relevant differences in their spatial distribution when $p$ is changed.

Finally, it would be very interesting to study if a similar pattern is observed in the one-dimensional clock model with a conserved order parameter. Concerning the value of the growth exponent $z$, which in the non-conserved case considered here effectively discriminate the Ising dynamics with $z=2$ from the XY behavior with $z=4$, in the conserved case one should observe a crossover from $z=3$ to $z=6$ [@Bray94; @Rutenberg95].

[**Acknowledgment**]{}

We acknowledge the referee for valuable suggestions.

This work has been partially supported from INFM through PAIS and from 