Abstract
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) = 2 nM( 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.
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