Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom

Details Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom

2000-08-30

arxiv.org/abs/hep-lat/0008024v2

Phys.Rev. D64 (2001) 065006

Physics

High Energy Physics

High Energy Physics - Lattice

18 pages, 8 figures Color coding in Fig. 5 changed to improve visibility

Scientific paper

10.1103/PhysRevD.64.065006

We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.

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