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Anisotropic perturbations in three-dimensional O(N)-symmetric vector models

We investigate the effects of anisotropic perturbations in three-dimensional O(N)-symmetric vector models. In order to assess their relevance for the critical behavior, we determine the renormalization-group dimensions of the anisotropic perturbations associated with the first few spin values of the representations of the O(N) group, because the lowest spin values give rise to the most important effects. In particular, we determine them up to spin 4 for N=2,3,4, by finite-size analyses of Monte Carlo simulations of lattice O(N) models, achieving a significant improvement of their accuracy. These results are relevant for several physical systems, such as density-wave systems, magnets with cubic symmetry, and multicritical phenomena arising from the competition of different order parameters.