A COMPARISON OF NUMERICAL ALGORITHMS FOR DYNAMICAL FERMIONS

The Langevin algorithm with bilinear noise and the hybrid Monte Carlo algorithm for dynamical fermions are applied to the simulation of the two-dimensional Gross-Neveu model with Wilson fermions. The hybrid Monte Carlo algorithm is implemented both with the classical "leap-frog" and with a new improved discretization scheme. The results are compared to theoretical predictions obtained by 1/N expansion and to previous simulations based on the pseudo-fermion algorithm. In the determination of the chiral transition point the three algorithms behave quite differently, and only the hybrid Monte Carlo method gives satisfactory results. The three methods are essentially equivalent in the evaluation of vacuum expectation values in a definite physical phase. © 1990.