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Beta functions of O$(N)$ model

Physics Asked on January 7, 2021

Consider the O$(N)$ model in $d$-dimensions given by:

$$L = frac{1}{2} (partial_{mu} phi)^2 – sum_{n} frac{g_{2n}}{(2n)!} phi^{2n} $$

Is there a reference where the beta functions $(beta_{g_{2i}})$ of this model is calculated for general $n$, in general $d$? In particular, I wanted to verify my beta functions for $g_6$ and $g_8$.

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