New universality classes for two-dimensional σ-models

We argue that the two-dimensional O(N)-invariant lattice σ-model with mixed isovector-isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum σ-model constructed by conventional perturbation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for N=3,4 on lattices up to 512×512, using a Wolff-type embedding algorithm. The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the ${\mathrm{RP}}^{\mathit{N}\mathrm{-}1}$ and N-vector models do not lie in the same universality class.