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

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.