A systematic calculation of the effective potential, renormalization, the nontrivial ultraviolet fixed point, and dynamical symmetry breaking in four-fermion theories in space-time dimension $2<D<\mathrm{}4\mathrm{}$ is presented up to next-to-the-leading order in the $\frac{1}{N}$ expansion. It is shown that the order-$\frac{1}{N}$ correction definitely increases the anomalous dimension of the composite operator $\overline{\Psi }\Psi$ at the fixed point. Some general conclusions on the relation between nontrivial fixed points and the phase transitions in dynamical symmetry breaking are also given.

• Received 22 April 1991

DOI:https://doi.org/10.1103/PhysRevD.45.4610