Effective potential, renormalization, and nontrivial ultraviolet fixed point in D-dimensional four-fermion theories (2<D<4) to order 1/N in 1/N expansion

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<4 is presented up to next-to-the-leading order in the 1/N expansion. It is shown that the order-1/N correction definitely increases the anomalous dimension of the composite operator bar ΨΨ 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