  We compute critical exponents of O(N) models in fractal dimensions between
two and four, and for continuos values of the number of field components N, in
this way completing the RG classification of universality classes for these
models. In d=2 the N-dependence of the correlation length critical exponent
gives us the last piece of information needed to establish a RG derivation of
the Mermin-Wagner theorem. We also report critical exponents for multi-critical
universality classes in the cases N>1 and N=0. Finally, in the large-N limit
our critical exponents correctly approach those of the spherical model,
allowing us to set N~100 as threshold for the quantitative validity of leading
order large-N estimates.
