written as G\_n(r,t)=\_i (n)\_j (n)= P\_i(n,t)P\_[i,j]{}(n,tn,t), \[appe4\] where the probabilities are defined analogously to the those of the clock model introduced above. Recognizing $G_n(r,t)$ in the last term of the right hand side of Eq. (\[appe3\]) one arrives at G(r,t)= -+ \_[n=1,3]{}G\_n(r,t). \[resul\] Because of the rotational symmetry one has $G_P(r,t)=G_n(r,t)$ for all values of $n$ and then one recovers Eq. (\[maj1\]).

[99]{}

A.J. Bray, Adv.Phys. [**43**]{}, 357 (1994).

R.J. Glauber, J.Math.Phys. [**4**]{}, 294 (1963).

A.D. Rutenberg and A.J. Bray, Phys.Rev.Lett. [**74**]{}, 3836 (1995).

F. Leyvraz and N. Jan, J.Phys.A: Math.Gen. [**19**]{}, 603 (1986).

C. Sire and S.N. Majumdar, Phys.Rev.Lett. [**74**]{}, 4321 (1995); Phys.Rev.E [**52**]{}, 244 (1995).

F. Liu and G.F. Mazenko, Phys.Rev.B [**47**]{}, 2866 (1993).

E. Lippiello and M. Zannetti, Phys.Rev. E [**61**]{}, 3369 (2000).

E. Lippiello, F. Corberi, and M. Zannetti, Phys.Rev.E [**71**]{}, 036104 (2005). Here the algorithm for the computation of the response function was obtained making explicit reference for simplicity to the case $p=2$, but the same derivation applies as well to generic $p$.

As for the first action, other possible moves require a larger activation energy and are, therefore, suppressed at low temperatures.

In a texture there may be several adjacent spins with the same 