Four loop renormalization of the Gross-Neveu model

Abstract

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

Operator mixing in the ε -expansion: Scheme and evanescent-operator independence

“…[18]. Since in this case the evanescent operators are first generated at three loops, we expect the whole evanescent tower to affect the Oðϵ 4 Þ term of the scaling dimension.…”

“…There are several examples of CFTs with fermionic degrees of freedom that can be studied in ϵ-expansion and to which the method we describe here is applicable, see for instance the recent works [18][19][20][21][22][23][24][25][26][27][28][29][30] and references therein. In our companion paper [31], we focus on 3d QED and use the NLO eigenvalues obtained here to estimate the scaling dimensions of four-fermion operators in d ¼ 3.…”

A functional perspective on emergent supersymmetry

“…In fact, there is a substantial body of literature on such models as they can give rise to critical phenomena where -in addition to the dimension and the symmetry of the (bosonic) order parameter -also the number and structure of the (fermionic) long-range degrees of freedom characterize the universal properties. Their quantitative determination has been pursued by a variety of methods including and 1/N expansions [16][17][18][19][20][21][22][23][24], Monte-Carlo simulations [17,[25][26][27][28][29][30][31][32][33], as well as the functional RG [34][35][36][37][38][39][40][41]. These models have recently received a great deal of attention as effective models describing phase transitions from a disordered (e.g., semi-metallic) to an ordered (e.g., Mott-insulating or superconducting) phase [2-4, 42, 43] In the present work, we investigate the emergence of supersymmetry in a (2+1) dimensional Yukawa-type model with a single Majorana fermion and a dynamical real scalar order parameter field.…”

Four-loop critical exponents for the Gross-Neveu-Yukawa models

“…However, despite this recent progress in MC simulations and the application of field-theoretical methods, the discrepancies between the results for the GN critical exponents have not been resolved and differences still show up in the first relevant digits. Concerning the pRG it can be stated that, with a few exceptions [42][43][44], most of the universality classes of the GNY models are only known up to two-loop order and no information about the behavior of higher-loop orders is available. This leaves quite some room for improvement on the estimates for critical exponents coming from the pRG.…”

“…(iii) Nonperturbative field-theoretical methods like the functional renormalization group (FRG) have achieved the maturity to provide quantitative estimates for critical exponents [37][38][39][40][41]. (iv) The perturbative renormalization group (pRG) has been formalized to a level that allows for feasible higher-loop calculations for these models [42][43][44]. However, despite this recent progress in MC simulations and the application of field-theoretical methods, the discrepancies between the results for the GN critical exponents have not been resolved and differences still show up in the first relevant digits.…”