= Solution
The susceptibility is the integrated <connected correlation function>, up to a nonsingular field-normalization factor:
$$
\chi\propto\int d^dx\,G_c(\mathbf x),\qquad
G_c(\mathbf x)=\langle m(\mathbf x)m(0)\rangle-\langle m\rangle^2.
$$
Above the transition at zero field the subtraction vanishes. In an ordered <thermodynamic phase> it is essential; integrating the disconnected constant would incorrectly give a <volume> divergence unrelated to the desired response.
With a microscopic cutoff $a$ and $r=|\mathbf x|$, radial integration and $u=r/\xi$ give
$$
\chi_s\propto S_d\int_a^\infty r^{1-\eta}g(r/\xi)\,dr
=S_d\xi^{2-\eta}\int_{a/\xi}^\infty u^{1-\eta}g(u)\,du.
$$
If $g(0)$ is finite, its large-distance tail decays sufficiently rapidly and $\eta<2$, the dimensionless integral approaches a finite nonzero constant. Thus
$$
\boxed{\chi_s\sim\xi^{2-\eta}\sim s^{-(2-\eta)\nu},\qquad\gamma=(2-\eta)\nu.}
$$
Short-distance contributions give a regular background. This is the <Fisher scaling relation>; it concerns the fluctuating connected part of the source <correlation> ansatz.
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