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We investigate the limits of effectiveness of classical spin simulations forpredicting free induction decays (FIDs) measured by solid-state nuclearmagnetic resonance (NMR) on systems of quantum nuclear spins. The specificlimits considered are associated with the range of interaction, the size ofindividual quantum spins and the long-time behavior of the FID signals. Wecompare FIDs measured or computed for lattices of quantum spins (mainly spins1/2) with the FIDs computed for the corresponding lattices of classical spins.Several cases of excellent quantitative agreement between quantum and classicalFIDs are reported along with the cases of gradually decreasing quality of theagreement. We formulate semi-empirical criteria defining the situations, whenclassical simulations are expected to accurately reproduce quantum FIDs. Ourfindings indicate that classical simulations may be a quantitatively accuratetool of first principles calculations for a broad class of macroscopic systems,where individual quantum microscopic degrees of freedom are far from theclassical limit.

Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins