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. [CPU time ≈ 7 years IBM RS-6000/320H] The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the RPN−1 and N-vector models do not lie in the same universality class.
@article{arxiv.hep-lat/9307022,
title = {New Universality Classes for Two-Dimensional $\sigma$-Models},
author = {Sergio Caracciolo and Robert G. Edwards and Andrea Pelissetto and Alan D. Sokal},
journal= {arXiv preprint arXiv:hep-lat/9307022},
year = {2009}
}