Scaling Function for Critical Scattering

The zero-field, two-point correlation function of an $n$-vector system in $d=4-\epsilon$ dimensions is calculated to order ${\epsilon }^2$ for $T>~T_c$. The scaling function is obtained as a closed, cutoff-independent integral. As $t=\frac{(T-T_c)}{T_c}\to 0$ at fixed wave vector $q$, the leading variation is ${{\hat{E}}_1}^{n,d}\mathrm{}\left(q\right)\mathrm{}{t}^{1-\alpha }+{{\hat{E}}_2}^{n,d}\mathrm{}\left(q\right)t$, where $\alpha$ is the specific-heat exponent; thence the maximum in the scattering above $T_c$ is located, in good agreement with high-$T$ series-expansion estimates.