긴즈버그 기준

식 $(3.26)$ $$\Delta C = \frac{T_{c}^{2}a_{2}^{\prime}^{2}}{2a_{4}}$$

식 $(3.39)$ \begin{equation}\notag \begin{split} C&=n\left[\frac{1}{2}\left(\frac{Ta_{2}^{\prime}^{2}}{c}^\right){2}(2\pi)^{-d}\int d^{d}k^{\prime}(1+k^{\prime}^{2})^{-2}\right]\xi^{4-d}+l.s \\ &\equiv C_{0}\xi^{4-d}+l.s \end{split} \end{equation}

$$C_{0}\approx\left(\frac{Ta_{2}^{\prime}}{c}\right)^{2}(2\pi)^{2}$$ 로 두고 $\xi^{-1}\equiv\left(\frac{a_{2}^{\prime}}{c}\right)^{\frac{1}{2}}|T-T_{c}|^{\frac{1}{2}}$을 사용하여 $\frac{C_{0}\xi^{4-d}}{\Delta C}$을 계산해보면

\begin{equation}\notag \begin{split} \frac{C_{0}\xi^{4-d}}{\Delta C} &\approx \left(\frac{Ta_{2}^{\prime}^{2}}{c}\right)^{2}(2\pi)^{-d}\left(\frac{a_{2}^{\prime}}{c}\right)^{\frac{d}{2}-2}|T-T_{c}|^{\frac{d}{2}-2}\frac{1}{\Delta C} \\ &=T^{2}a_{2}^{\prime}^{\frac{d}{2}}(2\pi)^{-d}a_{2}^{\prime}^{\frac{d}{2}-2}c^{-\frac{d}{2}}T_{c}^{\frac{d}{2}-2}\left|1-\frac{T}{T_{c}}\right|^{\frac{d}{2}-2}\frac{1}{\Delta C} \\ &=\frac{T^{2}a_{2}^{\prime}^{\frac{d}{2}}(2\pi)^{-d}c^{-\frac{d}{2}}T_{c}^{\frac{d}{2}-2}\frac{1}{\Delta C}}{\left|1-\frac{T}{T_{c}}\right|^{2-\frac{d}{2}}} \\ &=\left[\frac{\left\{T^{2}a_{2}^{\prime}^{\frac{d}{2}}(2\pi)^{-d}c^{-\frac{d}{2}}T_{c}^{\frac{d}{2}-2}\frac{1}{\Delta C}\right\}^{\frac{2}{4-d}}}{\left|1-\frac{T}{T_{c}}\right|}\right]^{2-\frac{d}{2}} \\ &=\left[\frac{\left\{\left(\frac{T}{T_{c}}\right)^{2}(2\pi)^{-d}\left(\frac{a_{2}^{\prime}T_{c}}{c}\right)^{\frac{d}{2}}\frac{1}{\Delta C}\right\}^{\frac{2}{4-d}}}{\left|1-\frac{T}{T_{c}}\right|}\right]^{2-\frac{d}{2}} \\ &\approx\left[\frac{\left\{(2\pi)^{-d}\left(\frac{a_{2}^{\prime}T_{c}}{c}\right)^{\frac{d}{2}}\frac{1}{\Delta C}\right\}^{\frac{2}{4-d}}}{\left|1-\frac{T}{T_{c}}\right|}\right]^{2-\frac{d}{2}} \end{split} \end{equation} 를 얻는다. 이제 \begin{equation}\notag \zeta_{T}\equiv\left[\frac{(2\pi\xi_{0})^{-d}}{\Delta C}\right]^{\frac{2}{4-d}},\quad\xi_{0}\equiv\left(\frac{c}{a_{2}^{\prime}{T_{c}}\right)^{\frac{1}{2}} \end{equation} 로 정의하고 다시 적어보면 \begin{equation}\notag \frac{C_{0}\xi^{4-d}}{\Delta C}\approx\left[\frac{\zeta_{T}}{\left|1-\frac{T}{T_{c}\right|}\right]^{2-\frac{d}{2}} \end{equation} 이 된다.