Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class

Abstract

We compute the large $N$ critical exponents $\eta$, $\eta_\phi$ and $1/\nu$ in $d$-dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of $1/N$. For instance, the large $N$ conformal bootstrap method is used to determine $\eta$ at $O(1/N^3)$ while the other exponents are computed to $O(1/N^2)$. Estimates of the exponents for a phase transition in graphene are given which are shown to be commensurate with other approaches. In particular the behaviour of the exponents in $2$ $<$ $d$ $<$ $4$ is in qualitative agreement with a functional renormalization group analysis. The $\epsilon$-expansion of the exponents near four dimensions are in agreement with recent four loop perturbation theory.