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| -rw-r--r-- | topology.tex | 16 |
1 files changed, 14 insertions, 2 deletions
diff --git a/topology.tex b/topology.tex index 8c21ee9..84b871d 100644 --- a/topology.tex +++ b/topology.tex @@ -117,13 +117,25 @@ $\mathbb M(1)=\frac1N\phi(1)\cdot\mathbf x_0$, the result is \overline{\chi}&=\int d\mathbb Q\,d\mathbb M\,d\sigma_0\,\exp\Bigg\{ \frac N2\log\operatorname{sdet}(\mathbb Q-\mathbb M\mathbb M^T) -\frac M2\log\operatorname{sdet}f(\mathbb Q) \notag \\ - &\qquad+N\int d1\,\left[ - \mathbb M(1)+\frac12\sigma_0(1)\big(\mathbb Q(1,1)-1\big) + &+N\int d1\,\left[ + (1+\hat\beta\bar\theta_1\theta_1)\mathbb M(1)+\frac12\sigma_0(1)\big(\mathbb Q(1,1)-1\big) \right] \Bigg\} \end{align} \begin{equation} + 0=\int d2\,(\mathbb Q(1,2)-\mathbb M(1)\mathbb M(2)^T)(1+\bar\theta_2\theta_2\hat\beta)+\mathbb M(1) +\end{equation} + +\[ + D=\beta R + \quad + \beta=-\frac{m+\sum_aR_{1a}}{\sum_aC_{1a}} + \quad + \hat m=0 +\] + +\begin{equation} \begin{aligned} &\frac1N\log\overline\chi =\frac12\Bigg[ |