Suppression of the Goldstone boson in a Gross-neveu model

We calculate to order $\frac{1}{N}$ the effective potential for two $N$-component massless fermion theories in two space-time dimensions. The order-one approximation to the effective potential predicts symmetry breaking for both theories. The order-$\frac{1}{N}$ approximation leads to discrete-symmetry violation, but the continuous-symmetry model is no longer broken, in agreement with a general theorem. The complete $\frac{1}{N}$ expansion is then reformulated in terms of vacuum graphs involving resummed propagators and nonlocal vertices. The l th-order contribution then involves only a finite number of graphs, each having $l$ loops.