Fisher scaling relation ($\gamma =(2-\eta )\nu$)

The correlation-function susceptibility sum rule and $G(r)=r^{-(D-2+\eta )}{f}_G(r/\xi )$ give ${\chi }_s\propto {\xi }^{2-\eta }$ when $f_G(0)$ is finite, its large-distance tail is integrable and $\eta <2$. With correlation-length critical exponent $\nu$, this gives the displayed relation for the magnetic-susceptibility critical exponent. Microscopic distances contribute a regular background rather than the divergent critical power.