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Several years ago it was found that perturbation theory for two-dimensionalO(N) models depends on boundary conditions even after the infinite volume limithas been taken termwise, provided $N>2$. There ensued a discussion whether theboundary conditions introduced to show this phenomenon were somehow anomalousand there was a class of `reasonable' boundary conditions not suffering fromthis ambiguity. Here we present the results of some computations that may beinterpreted as giving some support for the correctness of perturbation theorywith conventional boundary conditions; however the fundamental underlyingquestion of the correctness of perturbation theory in these models and inparticular the perturbative $\beta$ function remain challenging problems ofmathematical physics.Comment: 4 pages, 3 figure

Some new results on an old controversy: Is perturbation theory the correct asymptotic expansion in non-Abelian models?