= Gaussian free-energy scaling relation
{c}
{title2=$F=F_{\mathrm{shell}}+b^{-d}F(t^{\prime},h^{\prime})$}
For a stable massive <Gaussian field theory>, a finite blocking step yields $F(t,h)=F_{\mathrm{shell}}(t)+b^{-d}F(b^2t,b^{(d+2)/2}h)$ 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.
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