  The basic features of the slow relaxation phenomenology arising in phase
ordering processes are obtained analytically in the large $N$ model through the
exact separation of the order parameter into the sum of thermal and
condensation components. The aging contribution in the response function
$\chi_{ag}(t,t_w)$ is found to obey a pattern of behavior, under variation of
dimensionality, qualitatively similar to the one observed in Ising systems.
There exists a critical dimensionality $(d=4)$ above which $\chi_{ag}(t,t_w)$
is proportional to the defect density $\rho_D(t)$, while for $d<4$ it vanishes
more slowly than $\rho_D(t)$ and at $d=2$ does not vanish. As in the Ising
case, this behavior can be understood in terms of the dependence on
dimensionality of the interplay between the defect density and the effective
response associated to a single defect.
