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arXiv · 2507.22594

Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops

J. A. Gracey·A. Maier·P. Marquard·Y. Schröder
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Abstract

We renormalize the Gross-Neveu-Yukawa model with an $O(N)$ symmetry to $\mathcal{O}(ε^5)$ in $d=4-ε$ dimensions and determine the anomalous dimensions of the fermion and scalar fields, $β$-functions as well as the scalar field's mass operator. These are used to construct several $N$ dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when $N=2$. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when $N=1$, as well as for $N=5$ are also given to compare with results from other techniques such as the conformal bootstrap.

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J. A. Gracey, A. Maier, P. Marquard, Y. Schröder. 2025-07-30. Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops. https://arxiv.org/abs/2507.22594

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