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arXiv · 1709.05057

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

Nikolai Zerf·Luminita N. Mihaila·Peter Marquard·Igor F. Herbut·Michael M. Scherer
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Abstract

We study the chiral Ising, the chiral XY and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in $4-\epsilon$ dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order $\mathcal{O}(\epsilon^4)$. Further, we provide Pad\'e estimates for the correlation length exponent, the boson and fermion anomalous dimension as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with $N=1/4$ and $N=1/2$ fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

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Nikolai Zerf, Luminita N. Mihaila, Peter Marquard, Igor F. Herbut, Michael M. Scherer. 2017-09-15. Four-loop critical exponents for the Gross-Neveu-Yukawa models. https://doi.org/10.1103/physrevd.96.096010

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