  The three-dimensional SU(3) spin model is an effective Polyakov loop model
for QCD at nonzero temperature and density. It suffers from a sign problem at
nonzero chemical potential. We revisit this model using complex Langevin
dynamics and assess in particular the justification of this approach, using
analyticity at small mu^2 and the criteria for correctness developed recently.
Finite-stepsize effects are discussed in some detail and a higher-order
algorithm is employed to eliminate leading stepsize corrections. Our results
strongly indicate that complex Langevin dynamics is reliable in this theory in
both phases, including the critical region. This is in sharp contrast to the
case of the XY model, where correct results were obtained in only part of the
phase diagram.
