Correction to four-loop RG functions in the two-dimensional lattice 0(n) σ-model Original Research Article

We report on the numerical evaluation of the basic integrals appearing in the analytic results of the four-loop renormalization group functions in the two-dimensional lattice O(n) σ-model by Caracciolo and Pelissetto. In the list of integrals used for determining those functions, we find that two entries were not correctly evaluated. We give the corrected values including those for all other integrals which we computed with higher precision. These results are then applied to revise the determination of the second analytic correction to the correlation length ξ and spin susceptibility χ by Caracciolo et al. as well as our determination of the mass gap by means of a finite volume technique where we explicitly made use of the four-loop β-function. In both cases we find sizable changes in predictions.