Double scaling limits, Airy functions and multicritical behaviour in O(N) vector sigma models

O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N --> infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a generalised Airy function in the case of spacetime dimension zero and the partition function of a scalar field theory for positive spacetime dimension. Susceptibility matrices and beta functions are calculated.