to L(t)\~t\^, \[ldit\] with $z=2$. The same value is also expected [@Leyvraz86] for $p\le 4$.

The situation is different in the XY model in $d=1$. Here the order parameter is a vector which can gradually rotate with a low energy cost. A smooth $2\pi $ rotation of the phase $\theta $ is called a texture when the rotation is clockwise, or antitexture when it is counterclockwise. The length over which this phase winding occurs will be denoted by $L_w(t)$. After a quench from a disordered state textures and antitextures are formed with equal probability. Then, there are points where the rotation of $\theta $ changes direction and the phase decohere. We denote with $L_c(t)$ the characteristic length over which the phase remains coherent. It was shown [@Rutenberg95] that $L_w(t)$ and $L_c(t)$ grow with a power law (\[ldit\]) but with different exponents. Specifically one has $z=4$ for $L_w(t)$ and $z=2$ for $L_c(t)$. The existence of these two lengths is at the heart of the scaling violations of the XY model.

Characteristic lengths can be estimated from the knowledge of the two-points equal time correlation function G(r,t)=\_i(t) \_[i+r]{}(t) , \[gdir\] where $\langle \dots \rangle$ means an ensemble average, namely taken over different 