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[en] Using the standard 1/N expansion, we study supersymmetric O(N) vector models with an arbitrary potential in zero dimensions and discuss the nature and form of the critical behavior. We show that a double-scaling limit exists as in the case of matrix models and in bosonic vector models. We find in general a hierarchy of critical supersymmetric theories labeled by an integer k. The universal partition function of the kth theory is constructed from the effective action in the double-scaling limit
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