= Matching the amplitude of a massive critical correlation tail
{title2=$G(r)\sim\xi^{-\eta}\frac{\xi}{(r\xi)^{(D-1)/2}}e^{-r/\xi}$}
A <connected correlation function> with critical <anomalous dimension> $\eta$ scales as $G(r)=\xi^{-(D-2+\eta)}\mathcal G(r/\xi)$. If its large-distance shape is $s^{-(D-1)/2}e^{-s}$, substitution of $s=r/\xi$ produces the displayed amplitude. The extra $\xi^{-\eta}$ relative to the <massive Gaussian field correlation tail> is necessary for matching at $r$ of order $\xi$. Integrating over space gives <magnetic susceptibility> proportional to $\xi^{2-\eta}$; omitting that factor would instead make the long-distance contribution scale as $\xi^2$.
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