Multicritical Ginzburg ratio (source code)

= Multicritical Ginzburg ratio
{title2=$\langle(\delta M)^2\rangle_\xi/M^2\sim|t|^{(D-2)/2-1/(n-1)}$}

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.