  We have performed a high statistics Monte Carlo simulation to investigate
whether the two-dimensional O(n) non-linear sigma models are asymptotically
free or they show a Kosterlitz- Thouless-like phase transition. We have
calculated the mass gap and the magnetic susceptibility in the O(8) model with
standard action and the O(3) model with Symanzik action. Our results for O(8)
support the asymptotic freedom scenario.
