  We investigate the limits of effectiveness of classical spin simulations for
predicting free induction decays (FIDs) measured by solid-state nuclear
magnetic resonance (NMR) on systems of quantum nuclear spins. The specific
limits considered are associated with the range of interaction, the size of
individual quantum spins and the long-time behavior of the FID signals. We
compare FIDs measured or computed for lattices of quantum spins (mainly spins
1/2) with the FIDs computed for the corresponding lattices of classical spins.
Several cases of excellent quantitative agreement between quantum and classical
FIDs are reported along with the cases of gradually decreasing quality of the
agreement. We formulate semi-empirical criteria defining the situations, when
classical simulations are expected to accurately reproduce quantum FIDs. Our
findings indicate that classical simulations may be a quantitatively accurate
tool of first principles calculations for a broad class of macroscopic systems,
where individual quantum microscopic degrees of freedom are far from the
classical limit.
