Scaling of the linear response in simple ageing systems without disorder

The time-dependent scaling of the thermoremanent and zero-field-cooled susceptiblities in ferromagnetic spin systems undergoing ageing after a quench to a temperature at or below criticality is studied. A recent debate on their interpretation is resolved by showing that for systems with a short-ranged equilibrium spin-spin correlator and above their roughening temperature, the field-cooled susceptibility $\chi_{\rm FC}(t)-\chi_0\sim t^{-A}$ where $\chi_0$ is related to the equilibrium magnetization and the exponent A is related to the time-dependent scaling of the interface width between ordered domains. The same effect also dominates the scaling of the zero-field-cooled susceptibility $\chi_{\rm ZFC}(t,s)$, but does not enter into the thermoremanent susceptibility $\rho_{\rm TRM}(t,s)$. However, there may be large finite-time corrections to the scaling of $\rho_{\rm TRM}(t,s)$ which are explicitly derived and may be needed in order to extract reliable ageing exponents. Consistency with the predictions of local scale invariance is confirmed in the Glauber-Ising and spherical models.