# renormalization group in d=3

Do we really understand why the renormalization group in $d=2+\varepsilon$ and $d=4-\varepsilon$ taking $\varepsilon=1$ gives "good" values for critical exponents in $d=3$? Are they exceptions?
Is it also the case in high energy physics (particle, string, quantum gravity)?

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I would say we do for $4-\epsilon$, but $2+\epsilon$ is something I don't know. Where do you start for calculating Ising critical exponents in 2d? The 2d fixed points are special, and their perturbation theory doesn't seem to me to be an easy link to 3d. What's a reference for $2+\epsilon$? –  Ron Maimon Apr 30 '12 at 4:48