On the connection between off-equilibrium response and statics in non disordered coarsening systems

The connection between the out of equilibrium linear response function and static properties established by Franz, Mezard, Parisi and Peliti for slowly relaxing systems is analyzed in the context of phase ordering processes. Separating the response in the bulk of domains from interface response, we find that in order for the connection to hold the interface contribution must be asymptotically negligible. How fast this happens depends on the competition between interface curvature and the perturbing external field in driving domain growth. This competition depends on space dimensionality and there exists a critical value $d_c=3$ below which the interface response becomes increasingly important eventually invalidating the connection between statics and dynamics as the limit $d=1$ is reached. This mechanism is analyzed numerically for the Ising model with $d$ ranging from 1 to 4 and analytically for a continuous spin model with arbitrary dimensionality.