Is there any statement known about the anomalous dimensions of the $O(N)$ model in various dimensions and/or in the large-N limit?

If a $\phi^4$ ("double-trace") term is coupled to an $O(N)$ model then is there an argument as to why this quartic term is ignorable?

[..I believe that there are analogous statements known for higher bosonic spin fields too - at least for the second question of mine..]

I would be happy to see some pedagogic references which hopefully derive these.

This post imported from StackExchange Physics at 2014-03-07 13:38 (UCT), posted by SE-user user6818