different length scales. Moreover, the high–energy walls that are much further apart from each other than the low–energy ones, are also less stable. As a consequence, we expect direction–dependent scaling laws to hold for the structure factors $S_{\alpha}(\vec{k},t)$. This is made explicit by considering the functions $S_{\parallel}$ and $S_{\perp}$ introduced in Eqs. 4 and 5. Due to their definitions we expect these structure factors to obey scaling laws for one–dimensional and two–dimensional systems, respectively. This is verified by our simulations at $T_f=0.5465\,T_0$, i. e. in the case of continuous ordering. As shown by the $1d$ and $2d$ scaling plots in Figs. 6a and 6b, the data taken for a number of times $t\ge 500$ MCS after the quench indeed collapse onto single master curves. Moreover, the decay of both quantities at large k appears to be consistent with Porod’s law in $d=1$ and $d=2$, respectively,[@Porod; @comF]

$$k_{\parallel}(t)S_{\parallel}(k,t) 
   \propto (k/k_{\parallel}(t))^{-2},$$

$$k_{\perp}^2(t)S_{\perp}(k,t) \propto (k/k_{\perp}(t))^{-3} .$$

We now ask whether the same scaling laws apply to the results for $T_f>T_{sp}$, i. e. to the case of thermally activated ordering. Figure 8 contains the corresponding plots of $S_{\parallel}(k,t)$, part (a), and $S_{\perp}(k,t)$, part (b), calculated for $T_f=0.972\,T_0$ at times $t>\tau_{inc}$. In both parts of 