Unexpected results in asymptotically free quantum field theories

Abstract

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.

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

Cited by in corpus (17)

• The Nf=0 heavy quark potential from short to intermediate distances
• Testing the fixed-point QCD action and the construction of chiral currents
• Towards the continuum limit of a $(1+1)$d quantum link Schwinger model
• Lattice 2001: Reflections
• Asymptotically free models and discrete non-Abelian groups
• Nonstandard Cutoff Effects in the Nonlinear Sigma Model
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Qubitization strategies for bosonic field theories
• Universality of a truncated sigma-model
• Cutoff Effects in O(N) Nonlinear Sigma Models
• The continuum limit of the quark mass step scaling function in quenched lattice QCD
• Numerical confirmation of analytic predictions for the finite volume mass gap of the XY-model
• Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom
• Spin models on Platonic solids and asymptotic freedom
• Helicity modulus as renormalized coupling in the O(3) sigma-model
• Comparison of analytic and numerical results in the XY-model
• Counting gauge-invariant states with matter fields and finite gauge groups