a later Ising-like behavior.

Our results are at odd with what is found in Ref. [@Liu93] where an approximate analytical solution of the clock model in arbitrary dimension is obtained, finding an analogous scaling behavior for all $p< \infty $ but with $p$-dependent scaling functions. In the present one-dimensional case, instead, the situation is the opposite. There is not an analogous scaling behavior for all values of $p$, but a qualitative difference occurs crossing $p_c$. In addition, when scaling holds, namely for $p\le p_c$, the scaling functions do not depend on $p$. We believe, however, the behavior of the system considered in this paper, to be peculiar. Actually, the different dynamics observed crossing $p_c$ is determined by the simultaneous presence of interfaces and textures. On the basis of the discussion of Sec. \[intro\] we expect a similar situation to be only realized in $N$-component vectorial models with discrete states and $N=d+1$, where extended defects without a core may exist. For instance, it would be very interesting to study if a similar pattern is observed in $d=2$ for a generalization of the clock model where a three component order parameter is only allowed to point on a finite number $p$ of 