 Gaussian free-energy scaling relation

For a stable massive Gaussian field theory, a finite blocking step yields $F(t,h)=F_{\mathrm{shell}}(t)+b^{-d}F(b^{2}t,b^{(d+2)/2}h)$ for free-energy density. The finite-step shell and measure terms are analytic backgrounds. Generic-dimension singular scaling is homogeneous after subtracting those backgrounds; resonances such as Gaussian free-energy logarithm at effective dimension two need additive logarithmic terms.