Ising and Gross-Neveu model in next-to-leading order

TL;DR

This paper applies advanced functional renormalisation group techniques to analyze the critical behavior of Ising and Gross-Neveu models, providing new estimates and comparing them with existing methods, especially relevant for condensed matter physics like graphene.

Contribution

It introduces a high-accuracy computational approach to derive beta functions for these models, including more operators than previous studies, and offers refined critical quantity estimates.

Findings

Estimates agree with prior RG studies for Ising model.

Gross-Neveu model results match lattice and large-Nf calculations for two fermions.

Discrepancies remain for single fermion flavor, indicating need for further research.

Abstract

We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the beta functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudo-spectral methods to guarantee high accuracy. New estimates on critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalisation group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large-$N_f$ calculations, but for a single flavour, different methods disagree quantitatively, and further studies are necessary.