  We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising
ferromagnets quenched to criticality, both for the long-range model and its
short-range analogue in the limit of large dimension. Our exact solution shows
that, for both models, $X^\infty=1/2$ if the system is unmagnetized while
$X^\infty=4/5$ if the initial magnetization is non-zero. This indicates that
two different classes of critical coarsening dynamics need to be distinguished
depending on the initial conditions, each with its own nontrivial FDR. We also
analyze the dependence of the FDR on whether local and global observables are
used. These results clarify how a proper local FDR (and the corresponding
effective temperature) should be defined in long-range models in order to avoid
spurious inconsistencies and maintain the expected correspondence between local
and global results; global observables turn out to be far more robust tools for
detecting non-equilibrium FDRs.
