process, while it is activated for $p>6$. In general, from Eq. (\[activationm\]) one has $\Delta E_p^{(m)}>0$ for $p>2+2m$. The accomplishment of an action requires a time [@nota2] t \_p \^[(m)]{}(T\_f)\^[-1]{}= {1+}, \[ttcross\] $w_p$ being the transition rates defined in Eq. (\[metropolis\]). The crossover time, namely the characteristic time after which textures are removed, is given by the sum of the times required for all the $p-1$ actions. It can be evaluated as \_p \^[cross]{}(T\_f)=\_[m=1]{}\^[p-1]{}t \_p\^[(m)]{}(T\_f). \[tcross\] In the limit $T_f\to 0$ the sum is dominated by the process with the largest activation energy \_p \^[cross]{}(T\_f0)=Sup \_[{m=1,p-1}]{}t \_p\^[(m)]{}(T\_f). The $Sup $ in this equation is obtained for $m=m^*$ given by m\^\* = {

[ll]{} 1 $for$ p &lt; 10\
$for$ p10

. where $[ x ]$ is the integer part of $x$. Then, in the low-$T$ limit one has \_p \^[cross]{}(T\_f0)=t \_p\^[m\^\*]{}(T\_f). In conclusion, for $p\le p_c$ no activated processes are required and the system immediately enters the Ising-like phase ordering behavior. For $p>p_c$, instead, the dynamics is initially of the XY type until, at $t\sim \tau _p^{cross}(T_f)$ there is a crossover to the Ising-like non-equilibrium behavior.

The crossover can be appreciated in Figs. \[figlengthT2\],\[figlengthT1\]. The former shows the behavior of 