Solution
= Solution
A scalar field of <scaling dimension> $\Delta_\phi$ has a scale-invariant <two-point correlation function> proportional to $|x|^{-2\Delta_\phi}$. Comparison with the stated form gives
$$
\boxed{\Delta_\phi=\frac{d-2+\eta}{2}}.
$$
The difference $\eta/2$ from the engineering value is the field's <anomalous dimension>, generated by fluctuations and interactions at a non-Gaussian <renormalization-group fixed point>.