Unexpected results in asymptotically free quantum field theories

Details Unexpected results in asymptotically free quantum field theories Unexpected results in asymptotically free quantum field theories

2000-06-21

arxiv.org/abs/hep-lat/0006021v2

Nucl.Phys. B596 (2001) 481-494

Physics

High Energy Physics

High Energy Physics - Lattice

16 pages, 7 figures, some omissions corrected, a reference added

Scientific paper

10.1016/S0550-3213(00)00696-9

We study the behavior of asymptotically free (AF) spin and gauge models when their continuous symmetry group is replaced by different discrete non-Abelian subgroups. Precise numerical results with relative errors down to O(0.1%) suggest that the models with large subgroups are in the universality class of the underlying original models. We argue that such a scenario is consistent with the known properties of AF theories. The small statistical errors allow a detailed investigation of the cut-off effects also. At least up to correlation lengths ~300 they follow effectively an O(a) rather than the expected O(a^2) form both in the O(3) and in the dodecahedron model.

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