A determination of the mass gap in the O(n) sigma model

Details A determination of the mass gap in the O(n) sigma model A determination of the mass gap in the O(n) sigma model

1996-11-06

arxiv.org/abs/hep-lat/9611006v2

Nucl.Phys. B496 (1997) 408-434

Physics

High Energy Physics

High Energy Physics - Lattice

31 pages, Latex, addition of a sentence in abstract by pointing out that the paper has been revised in hep-lat/9810025

Scientific paper

10.1016/S0550-3213(97)00197-1

We calculate the finite volume mass gap $M(L)$ at 3-loop level in the non-linear O($n$) $\sigma$-model in two dimensions in small volumes. By applying the Monte Carlo measurements of the running coupling $\bar g^2(L)=2nM(L)L/(n-1)$ by L\"uscher, Weisz and Wolff measured in units of the physical mass gap $m$, the result is used to determine $m$ in units of the $\Lambda$-parameter in the O(3) and O(4) models. Our determinations show good agreement with those by Hasenfratz, Maggiore and Niedermayer in both models. We note that this manuscript has been revised in our paper hep-lat/9810025 by using the corrected four-loop $\beta$-function on the lattice.

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