Comparative study of the Langevin and the hybrid algorithms for lattice gauge theory simulations

A comparative study was made for the Langevin and hybrid simulations for QCD both with and without dynamical fermions. It was found that for the choice of control parameters commonly used the Langevin method in 5-10 times more efficient than the other for the relaxation of the system, if it is measured in the scale of fictitious time, although this merit may be diminished by a larger systematic error which necessitates an extra effort to obtain bias-free results. Our analysis is also suggestive of the importance of the Langevin noise in the tunneling between two coexisting states close to a first-order phase transition. (orig.)