Higher orders in N?1 in the Gross-Neveu model

We study higher-order terms in the N expansion of the two-dimensional model field theory of Gross and Neveu. The quantity $\text{M}{}_{\mathrm{\sigma }}\text{2M}{}_{\mathrm{<mtext>F</mtext><mtext>?1</mtext>}}$ (M_F is the fermion mass, M_σ is the scalar bound-state mass), is conjectured to deviate from zero in O(N^?4). Order N^?1 corrections are found to leave unchanged both the symmetry-breaking, and the absence of zeros of the Callan-Symanzik function β for real non-zero coupling constant. Behavior of β for complex coupling constant is altered considerably by the corrections; consequences are discussed.We obtain the following additional results: proof that the model is renormalizable without the necessity of additional interactions; construction of a perturbation theory in the asymmetric vacuum; proof of a lemma on fermion-antifermion thresholds in two-dimensional space-time; derivation of closed formulae for arbitrary one-loop integrals in two-dimensional space-time.