Variational solution of the Gross-Neveu model: Finite N and renormalization

We show how to perform systematically improvable variational calculations in the O(2N) Gross-Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross-Neveu model, the numerical results obtained from a ''two-loop'' variational calculation are in a very good agreement with exact quantities down to low values of N.