$y=t/s$ and h(y)=. \[ccsc\] In the XY model, instead, one finds [@Rutenberg95] the stretched exponential behavior C(t,s)={-s\^ }, \[cxy\] This expression cannot be cast in a scaling form, as for the Ising model, revealing the absence of dynamical scaling.

Numerical results {#num}
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In the following we will present the numerical results. Setting $J=1$, for each case considered we simulated a string of $10^4$ spins with periodic boundary conditions and different values of $p$ ranging from $p=2$, corresponding to the Ising model, to $p=\infty$, corresponding to the XY model. We consider a single spin flip dynamics regulated by transition rates w{\[\]}=w\_p()= . \[metropolis\] Here $[\sigma]$ and $[\sigma']$ are the spin configurations before and after the move, differing at most by the value of the spin on a randomly chosen site, $\Delta E=H[\sigma']-H[\sigma]$, and we have set the Boltzmann constant to unity. The transition rates (\[metropolis\]) are a generalization of Glauber transition rates to the $p$-state spins of the clock model. They reduce to the usual Glauber transition rates $w\{[\sigma]\to [\sigma']\}=(1/2)[1+\tanh (-\Delta E/2T)]$ for $p=2$. The factor $2/p$ in Eq. (\[metropolis\]) ensures that all spin values have the same probability $1/p$ when $\Delta E=0$.

An average over $10^4$ realizations is made 