Four loop renormalization of the Gross-Neveu model

Understand

We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the 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.