Renormalizing the nonrenormalizable

A perturbatively nonrenormalizable variant of the Gross-Neveu model of Euclidean quantum field theory with bare propagator p/p^2-ε is considered. We outline a rigorous argument proving that by appropriate choice of the bare coupling constant the model may be renormalized nonperturbatively, which results in a theory governed at short distances by a non-Gaussian fixed point of the renormalization group.