 Multicritical Ginzburg ratio

For a tuned multicritical even Landau potential with leading positive $M^{2n}$ term, $M^2\sim |t{|}^{1/(n-1)}$ and $\xi \sim |t{|}^{-1/2}$. Long-wavelength Gaussian fluctuations in a correlation volume have variance proportional to ${\xi }^{2-D}$. Their ratio to $M^2$ therefore scales as $|t{|}^{(D-2)/2-1/(n-1)}$, vanishing only for $D>2n/(n-1)$. At equality the criterion is marginal, requiring further fluctuation analysis.