theory was used to show the dependence of $g(x)$ on $p$. However, the approximation used in [@Liu93] is expected to improve increasing the dimensionality $d$.

The cases with $p>p_c$ are shown in Fig. \[figg2\],\[figg3\]. As discussed in Section \[model\], $G(r,t)$ obeys the scaling form (\[scalgferro\]) also in the XY model, although dynamical scaling is violated. According to our conjecture, for $p>p_c$ we expect the same behavior. In Fig. \[figg2\] it is shown that, indeed, the curves at different times collapse when plotted against $x=r/L_G(t)$. However, differently from the cases $p\le p_c$, the masterfunction $g(x)$ depends on $p$ and converges to the form (\[xystrutt\]) of the XY model for $p\to \infty $, as shown in Fig. \[figg3\].

Let us turn to consider the autocorrelation function, that is plotted in Figs. \[figauto1\]-\[figauto2\] against $y=t/s$. In Fig. \[figauto1\] the cases with $p=2,3,4$ are considered. Here the situation is analogous to that of $G(r,t)$. For $p=2$ one should find collapse of the curves with different $s$ on a mastercurve $h(y)$, Eq. (\[ccs\]). This is indeed observed in Fig. \[figauto1\]. The same behavior is observed also for $p=3,4$. Again, as for $G(r,t)$, we find that the mastercurves $h(y)$ are numerically indistinguishable for different $p$, and 