We investigate four-Fermi theories on 3-dimensional lattices. These are Gross-Neveu and Thirring models with a varying numbers of flavours $N_f$. These theories are renormalizable in the $1/N_f$-expansion and possess an interacting continuum limit. The Thirring models are closely related to 3-dimensional QED and serve as field-theoretic models for graphene. For sufficiently small $N_f$ they show a spontaneous breaking of chiral symmetry. The Gross-Neveu models undergo a second order phase transition for all values of $N_f$. We present results for the critical behaviour of these lattice models. Contrary to previous works we use chiral fermions for which the lattice models have exactly the same internal symmetries as the continuum models.

Applications Beyond QCD