Finite Volume Method for a Determination of Mass Gap in the Two Dimensional O(n) σ-Model

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. In order to determine the physical mass gap m for the limit of infinite volume, we first apply our results in O(∞) model where the mass gap can be calculated exactly. There, we find nice agreement of our perturbative determination for m with the analytic value. Motivated by the successful applicability of our method in O(∞) model, we make use of this method to determine the physical mass gap m in O(3) model by extrapolating the finite volume mass gap M(L) to the infinite volume.