(t,s)$, the cases with $p\le p_c$ have also the same parametric plot of $\chi (t,s)$ versus $C(t,s)$ [@Lippiello00].

The situation is radically different for $p>p_c$. We expect here to see a texture-dominated XY-like dynamics, with violations of dynamical scaling that can be detected from $C(t,s)$. In fact, this is what one observes in Fig. \[figauto2\], where the autocorrelation function is plotted against $y$. For each value of $p$, curves with different values of $s$ do not collapse. The whole behavior is qualitatively similar to that of the XY model described by Eq. (\[cxy\]), which predicts the lowering of the curves for fixed $y$ as $s$ increases. Quantitatively, as already observed regarding $G(r,t)$, the analytic form of the curves depends on $p$ and is different from that of the XY model, namely Eq. (\[cxy\]). As shown in Fig. \[figauto3\], Eq. (\[cxy\]) is gradually approached increasing $p$.

Quenches to $T_f>0$. {#Tnzer}
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When quenches to finite temperatures are considered, as already discussed in Sec. \[model\], one has a finite equilibration time $\tau _p^{eq}(T_f)$. In the following we will always discuss the ordering kinetics preceding the equilibration time, namely for $t\ll \tau _p^{eq}(T_f)$.

According to our hypothesis, the XY-like behavior observed for $p>p_c$ 