Four-fermion field theories and the Chern-Simons field: A renormalization group study - art. no. 027701

In 2+1 dimensions, we consider the model of an N-flavor, two-component ferm ionic field interacting through a Chern-Simons field in addition to a four- fermion self-interaction which consists of a Linear combination of the Gros s-Neveu- and Thining-like terms. The four-fermion interaction is not pertur batively renormalizable and the model is taken as an effective field theory in the region of low momenta. Using the Zimmerman procedure for reducing c oupling constants, it is verified that, for small values of the Chern-Simon s parameter, the origin is an infrared-stable fixed point but changes to ul traviolet stable as alpha becomes bigger than a critical alpha(c). Composit e operators are also analyzed and it is shown that a specific four-fermion interaction has an improved ultraviolet behavior as N increases. [S0556-282 1(99)00914-5].