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.