Is the 2D O(3) Nonlinear $σ$ Model Asymptotically Free?

Details Is the 2D O(3) Nonlinear $σ$ Model Asymptotically Free? Is the 2D O(3) Nonlinear $σ$ Model Asymptotically Free?

1997-06-13

arxiv.org/abs/hep-lat/9706011v1

Phys.Lett. B430 (1998) 314-319

Physics

High Energy Physics

High Energy Physics - Lattice

10 pages

Scientific paper

10.1016/S0370-2693(98)00528-0

We report the results of a Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $\sigma$ model. The notable finding is that it agrees very well with both the prediction inspired by Zamolodchikovs' S-matrix ansatz and with the continuum limit of the dodecahedron spin model. The latter finding renders the existence of asymptotic freedom in the O(3) model rather unlikely.

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