Abstract
We show that the recently observed essential singularity in the dimensionally regularized 1/ N expansion appears generaily in models having linear or quadratic divergences in the next·to-Ieading order of the 1/ N expansion and has nothing to do with the asymptotic freedom of the models. Also analytic regularization produces the same kind of the singularity as in dimensional regularization when used in the 1/ N expansion in O(N) (,P) ~~4 but not in O(N) non-linear (J model in two dimensions. This singularity is accompanied by the term depending on the renormalization mass scale which makes the minimal subtraction method unable to be carried out. Typical examples are the three-dimensional O(N) model with both bosons and fermions and (Yukawa)d~4 in addition to O(N) (~2)~~4.
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