The Gross-Neveu model and the pseudofermion algorithm

Precision tests of the pseudofermion method for numerical simulations of dynamical fermions on the lattice are performed using a new criterion for the control of systematic errors, based on the Schwinger-Dyson equations. A lattice version of the two-dimensional N fermion Gross-Neveu model, based on Wilson fermions and Symanzik's improvement scheme, is completely analyzed in the large-N expansion, up to O(1/N). An unambiguous definition for the perturbative part of operators mixing with the vacuum (''condensates'') is presented and discussed. Finite lattice effects are also examined. A Monte Carlo simulation of the model is performed for different values of the coupling in the scaling region, taking into account the effects of the variation of the simulation parameters. Comparison of analytical and numerical results shows a small but systematic difference, mainly due to an imprecise determination of the critical mass. (orig.)