Addendum: Long-range multi-scalar models at three loops

TL;DR

This paper corrects a previous three-loop beta function calculation for long-range multi-scalar models, providing updated critical exponents and detailed methodology for the correction process.

Contribution

It introduces a new method for computing a specific Feynman diagram in the three-loop beta functions and updates the critical exponents for several models.

Findings

Corrected the three-loop beta function calculation.

Provided updated critical exponents for multiple models.

Supplied Mathematica files for numerical evaluation.

Abstract

We correct the computation of one Feynman diagram in the three-loop beta functions for the long-range quartic multi-scalar model, originally presented in (2020 J. Phys. A: Math. Theor. 53 445008) [arXiv:2007.04603]. The correction requires the use of a different method than in the original paper, and we give here full details about the method. We then report the updated numerics for critical exponents of the Ising model, vector model, cubic model and bifundamental model. Mathematica files for the numerical evaluation of the corrected diagram are provided in ancillary.