A determination of the mass gap in the 0(n) σ-model Original Research Article

We calculate the finite volume mass gap M(L) at 3-loop level in the non-linear O(n) σ-model in two dimensions in small volumes. By applying the Monte Carlo measurements of the running coupling g−2 (L) = 2nM(L) L/(n - 1) by Lüscher, Weisz and Wolff measured in units of the physical mass gap m, the result is used to determine m in units of the Λ-parameter in the O(3) and O(4) models. Our determinations show good agreement with those by Hasenfratz, Maggiore and Niedermayer in both models.