Scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics

In this paper we investigate the relation between the scaling properties of the linear response function $R(t,s)$, of the thermoremanent magnetization (TRM) and of the zero field cooled magnetization (ZFC) in the context of phase ordering kinetics. We explain why the retrival of the scaling properties of $R(t,s)$ from those of TRM and ZFC is not trivial. Preasymptotic contributions generate a long crossover in TRM, while ZFC is affected by a dangerous irrelevant variable. Lack of understanding of both these points has generated some confusion in the literature. The full picture relating the exponents of all the quantities involved is explicitely illustrated in the framework of the large $N$ model. Following this scheme, an assessment of the present status of numerical simulations for the Ising model can be made. We reach the conclusion that on the basis of the data available up to now, statements on the scaling properties of $R(t,s)$ can be made from ZFC but not from TRM. From ZFC data for the Ising model with $d=2,3,4$ we confirm the previously found linear dependence on dimensionality of the exponent $a$ entering $R(t,s) \sim s^{-(1+a)}f(t/s)$. We also find evidence that a recently derived form of the scaling function $f(x)$, using local scale invariance arguments [M.Henkel, M.Pleimling, C.Godr\`{e}che and J.M.Luck, Phys.Rev.Lett. {\bf 87}, 265701 (2001)], does not hold for the Ising model.