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

TL;DR

This paper evaluates the effectiveness of complex Langevin dynamics in simulating the SU(3) spin model at nonzero chemical potential, demonstrating its reliability across different phases including the critical region.

Contribution

The study provides a thorough reassessment of complex Langevin dynamics for the SU(3) spin model, addressing justification, stepsize effects, and employing a higher-order algorithm for improved accuracy.

Findings

Complex Langevin dynamics is reliable for the SU(3) spin model across all phases.

Finite-stepsize effects can be mitigated with a higher-order algorithm.

Contrasts with the XY model show broader applicability of the method.

Abstract

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.