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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.
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