Generic features of the fluctuation dissipation relation in coarsening systems

The integrated response function in phase-ordering systems with scalar, vector, conserved, and nonconserved order parameter is studied at various space dimensionalities. Assuming scaling of the aging contribution ?ag(t,tw)=tw-a???(t/tw) we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing the dimensionality dependence of a? in all cases considered. The primary result is that a? vanishes continuously as d approaches the lower critical dimensionality dL. This implies that (i) the existence of a nontrivial fluctuation dissipation relation and (ii) the failure of the connection between statics and dynamics are generic features of phase ordering at dL.