Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided N>2. There ensued a discussion whether the boundary conditions introduced to show this phenomenon were somehow anomalous and there was a class of 'reasonable' boundary conditions not suffering from this ambiguity. Here we present the results of some computations that may be interpreted as giving some support

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... for the correctness of perturbation theory with conventional boundary conditions; however the fundamental underlying question of the correctness of perturbation theory in these models and in particular the perturbative β function remain challenging problems of mathematical physics.