Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited

A bstract 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 μ 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.