Discrete non-Abelian groups and asymptotically free models

Abstract

We consider a two-dimensional $\sigma$-model with discrete icosahedral/dodecahedral symmetry. Using the perturbative renormalization group, we argue that this model has a different continuum limit with respect to the O(3) $\sigma$ model. Such an argument is confirmed by a high-precision numerical simulation.

Comments: 5 pages including 6 postscript figures. Talk given at HEP01 in Budapest, Hungary, in July 2001