Is there any useful introductory material about the calculation of the beta function in $\phi^4$ scalar theory and $O(N)$ model? I would also like to generalize this to the large-$N$ limit.

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    $\begingroup$ Related, but unanswered: physics.stackexchange.com/q/578643 $\endgroup$ Jun 18 '21 at 11:57
  • $\begingroup$ You can write a few line long code in Mathematica, it's fairly simple then you can set your $N$, however since I was running the code in a 10 years old pc I couldn't go beyond $N=20$. $\endgroup$
    – Monopole
    Jun 18 '21 at 13:32
  • $\begingroup$ That sounds like a strange approach. The residue of $\frac{1}{\epsilon}$ in the dimensionally regularized 4pt function of $\phi^i$ is an analytic function of $N$. If you want $\frac{1}{N}$ to be the expansion parameter instead of $\epsilon$, have a look at 1404.1094. $\endgroup$ Jun 18 '21 at 14:00

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