# Resources on calculation of beta function for $\mathrm{O}(N)$ model

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.

• Related, but unanswered: physics.stackexchange.com/q/578643 Jun 18 '21 at 11:57
• 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 $N=20$. Jun 18 '21 at 13:32
• 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. Jun 18 '21 at 14:00