  The spin-dependent corrections to the static interquark potential are relevant to describing the fine and hyper-fine splittings of the heavy quarkonium spectra. We investigate these corrections in SU(3) lattice gauge theory with the Polyakov loop correlation function as the quark source by applying the multi-level algorithm. We observe remarkably clean signals for the spin-dependent potentials up to intermediate distances. 
Determination of the spin-dependent potentials with the multi-level   algorithm