Four loop renormalization of the Gross-Neveu model

Abstract

We renormalize the $SU(N)$ Gross-Neveu model in the modified minimal subtraction scheme at four loops and determine the $\ensuremath{\beta}$ function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-Fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.