sections we analyze in more detail the incubation time and the long time coarsening processes.

Incubation time \[INCUBATION\]
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In the preceding section we introduced the incubation time $\tau_{inc}$ as the characteristic time interval between the quench and the observed growth of ordered domains in the case of metastability, $T_f>T_{sp}$. Let us now look more precisely at the processes that take place in the system within the initial stages of ordering. One relevant quantity here is the excess energy, $\Delta E(t) = E(t) - E(\infty)$, defined as the difference between the actual energy of the system, $E(t)$, and the energy it would reach after complete equilibration, $E(\infty)$. This means that we identify $E(\infty)$ with the energy of a single ordered domain of the size of the whole system, equilibrated at $T_f$. In Figure 5a $\Delta E(t)$ per lattice site is shown for a number of final temperatures $T_f$. Initially, the relaxation of $\Delta E(t)$ depends on temperature only weakly. Then, after about 20 MCS, the curves in Fig. 5a split due to a considerable slowing down of the relaxation rate with growing temperature. In turn, for shallow quenches, ordering proceeds in three stages, as displayed already in Fig. 2c. First, 