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

J. A. Gracey*

A. Maier†

P. Marquard‡

Y. Schröder§

  • Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, United Kingdom

  • Centro de Ciencias Exactas, Departamento de Ciencias Básicas, Universidad del Bío-Bío, Avenida Andrés Bello 720, Chillán, Chile

  • *Contact author: gracey@liverpool.ac.uk
  • †Contact author: amaier@ifae.es
  • ‡Contact author: peter.marquard@desy.de
  • §Contact author: yschroder@ubiobio.cl
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Phys. Rev. D 112, 085029 – Published 30 October, 2025

DOI: https://doi.org/10.1103/lmpx-n3mj

Abstract

We renormalize the Gross-Neveu-Yukawa model with an O(N) symmetry to O(ε5) 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 semimetals 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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Phys. Rev. D 112, 085029– Published 30 October, 2025
  • Received 8 August 2025
  • Accepted 24 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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