Slow relaxation in the large N model for phase ordering

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.