긴즈버그 기준

식 $(3.26)$ $$ \Delta C = \frac{T_c^2{a_2^\prime}^2}{2a_4} $$

식 $(3.39)$ \begin{equation} \begin{split} C &= n \left[ \frac{1}{2} \left( \frac{Ta_2^\prime}{c} \right)^2 (2\pi)^-d \int d^dk^\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.