  In a conformal field theory with weakly broken higher spin symmetry, the
leading order anomalous dimensions of the broken currents can be efficiently
determined from the structure of the classical non-conservation equations. We
apply this method to the explicit example of $O(N)$ invariant scalar field
theories in various dimensions, including the large $N$ critical $O(N)$ model
in general $d$, the Wilson-Fisher fixed point in $d=4-\epsilon$, cubic scalar
models in $d=6-\epsilon$ and the nonlinear sigma model in $d=2+\epsilon$. Using
information from the $d=4-\epsilon$ and $d=2+\epsilon$ expansions, we obtain
some estimates for the dimensions of the higher spin operators in the critical
3d $O(N)$ models for a few low values of $N$ and spin.
