This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision |
| 김민재:스터디:임계현상:3장._가우스_근사 [2017/10/05 16:24] – minjae | 김민재:스터디:임계현상:3장._가우스_근사 [2023/09/05 15:46] (current) – external edit 127.0.0.1 |
|---|
| ⟨σik⟩=0,⟨σik⟩=0, | ⟨σik⟩=0,⟨σik⟩=0, |
| G(k)=⟨|σik|⟩2=12(a2+ck)−1,G(k)=⟨|σik|⟩2=12(a2+ck)−1, | G(k)=⟨|σik|⟩2=12(a2+ck)−1,G(k)=⟨|σik|⟩2=12(a2+ck)−1, |
| $$FL^{d}=a_{0}L^{d}-\frac{1}{2}T\sum_{k<\Lambda}n\ln\left[\frac{\pi}{(a_{2}+ck^{2})\right]\quad(F\equiv\frac{f}{L^{d}})$$ | $$FL^d=a_0L^d-\frac{1}{2}T\sum_{k<\Lambda}n\ln\left[\frac{\pi}{(a_2+ck^2)}\right]\quad\left(F\equiv\frac{f}{L^d}\right)$$ |
| 이 된다. 앞서, a2=a′2(T−Tc)라 두었기 때문에 | 이 된다. 앞서, a2=a′2(T−Tc)라 두었기 때문에 |
| limT→TcG(k)∝k−2, | limT→TcG(k)∝k−2, |
| \begin{equation}\notag | \begin{equation}\notag |
| \begin{split} | \begin{split} |
| C&\equiv -T\left(\frac{\partial^{2}F}{\partial T^{2}}\right) \\ | C&\equiv -T\left(\frac{\partial^2F}{\partial T^2}\right) \\ |
| &=\frac{a_{2}^{\prime}^{2}}{2}T^{2}n(2\pi)^{-d}\int d^{d}k(a_{2}+ck^{2})^{-2}+l.s | &=\frac{{a_2}^{\prime~2}}{2}T^2n(2\pi)^{-d}\int d^dk(a_2+ck^2)^{-2}+l.s |
| \end{split} | \end{split} |
| \end{equation} | \end{equation} |
| \begin{equation}\notag | \begin{equation}\notag |
| \begin{split} | \begin{split} |
| C&=n\left[\frac{a_{2}^{\prime}^{2}}{2}T^{2}(2\pi)^{-d}\int d^{d}k(a_{2}+ck^{2})^{-2}\right]+l.s \\ | C&=n\left[\frac{{a_2}^{\prime~2}}{2}T^2(2\pi)^{-d}\int d^dk(a_2+ck^2)^{-2}\right]+l.s \\ |
| &=n\left[\frac{a_{2}^{\prime}^{2}}{2}T^{2}(2\pi)^{-d}\int d^{d}\left(\frac{k^{\prime}}{\xi}\right)(c\xi^{-2}+ck^{\prime}^{2}\xi^{-2})^{2}\right]+l.s \\ | &=n\left[\frac{{a_2}^{\prime~2}}{2}T^{2}(2\pi)^{-d}\int d^{d}\left(\frac{k^\prime}{\xi}\right)(c\xi^{-2}+ck^{\prime}^{2}\xi^{-2})^{2}\right]+l.s \\ |
| &=n\left[\frac{1}{2}(Ta_{2}^{\prime})^{2}(2\pi)^{-d}c^{-2}\int d^{d}k^{\prime}(1+k^{\prime}^{2})^{-2}\right]\xi^{4-d}+l.s \\ | &=n\left[\frac{1}{2}(T{a_2}^\prime)^2(2\pi)^{-d}c^{-2}\int d^dk^\prime(1+k^{\prime~2})^{-2}\right]\xi^{4-d}+l.s \\ |
| &\equiv C_{0}\xi^{4-d}+l.s | &\equiv C_0\xi^{4-d}+l.s |
| \end{split} | \end{split} |
| \end{equation} | \end{equation} |