= Anisotropic Gaussian smectic scaling
{title2=$y_t=2,\quad y_h=(d+5)/4$}
For a Gaussian kernel $Kq_\parallel^2+Lq_\perp^4+t$, keeping both <gradient> coefficients fixed gives $q'_\parallel=bq_\parallel$ and $q'_\perp=b^{1/2}q_\perp$. The volume rescales by $b^{(d+1)/2}$. Fourier-field normalization is $m'(q')=m(q)/b^{(d+5)/4}$; the real-space normalization instead divides by $b^{(3-d)/4}$. The thermal coefficient scales by $b^2$ and the uniform source by $b^{(d+5)/4}$. Thus $\xi_\parallel\sim t^{-1/2}$, $\xi_\perp\sim t^{-1/4}$ and the formal Gaussian free-energy powers are $\alpha=(7-d)/4$, $\Delta=(d+5)/8$.
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