disordered phase (for $T>T_0$) to the $L1_2$–type ordered structure (for $T<T_0$). The correlation length of the disordered phase, $\xi$, remains finite at coexistence, and approximately fulfills the mean–field type relation $\xi^2(T) \propto 1/(T-T_{sp})$, with $T_{sp}<T_0$. In our previous work [@paper1] we found $T_{sp}= (0.967 \pm 0.003) T_0$ as the value best fitting our Monte Carlo data for the correlation length above $T_0$. Hence, within this procedure, our model displays a fairly well-defined temperature for the onset of spinodal ordering. A precise separation of the metastable (thermally activated ordering) from the unstable regime (continuous ordering), however, does not exist in systems with short–range interactions.[@BindStauf; @Bind2]

Below we demonstrate the role of that temperature deduced from equilibrium considerations, in non–equilibrium ordering processes. It turns out that for temperatures $T_f>T_{sp}$ and $T_f<T_{sp}$ two contrasting transition scenarios occur that lead to domain patterns typical of nucleation and spinodal ordering, respectively. We shall illustrate this by one example for each regime.

Let us start our description with thermally activated growth of the ordered phase, i. e. with the case of a shallow quench, $T_0>T_f>T_{sp}$. We then expect that the ordered regions – nuclei of the new phase – are repeatedly formed and destroyed by thermal 