Discussion of critical phenomena for generaln-vector models

We discuss, in the framework of the $\epsilon$ expansion, systems with an $n$-component order parameter and with the most general interaction compatible with the existence of only one length scale. At lowest order, it is found that the only stable fixed point corresponds to an $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$-symmetric interaction if $n$ is smaller that 4; in that case, two exponents only are sufficient to characterize deviations from scaling. If there is a second nontrivial fixed point, then a third one is always present; among these three fixed points, one and only one is stable.