  The spin-dependent corrections to the static inter-quark potential are
phenomenologically relevant to describing the fine and hyperfine spin splitting
of the heavy quarkonium spectra. We investigate these corrections, which are
represented as the field strength correlators on the quark-antiquark source, in
SU(3) lattice gauge theory. We use the Polyakov loop correlation function as
the quark-antiquark source, and by employing the multi-level algorithm, we
obtain remarkably clean signals for these corrections up to intermediate
distances of around 0.6 fm. Our observation suggests several new features of
the corrections.
