Four loop renormalization of the Gross-Neveu model

TL;DR

This paper performs a four-loop renormalization of the SU(N) Gross-Neveu model in the MSbar scheme, accurately accounting for evanescent operators and providing critical exponent estimates relevant to graphene phase transitions.

Contribution

It presents the first four-loop beta-function calculation for the Gross-Neveu model, including effects of evanescent operators, advancing theoretical understanding of its renormalization.

Findings

Calculated the four-loop beta-function in the MSbar scheme.

Accounted for evanescent 4-fermi operators affecting renormalization.

Provided estimates of critical exponents for graphene phase transitions.

Abstract

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.