基础

几何表象

$$\mathcal{Z}{\rm spin} = \sum $$} \prod_{\langle ij\rangle} e^{Ks_i s_j

$e^{Ks_is_j} = \cosh K \sum_{f=0}^1 (s_is_j \tanh K)^f,\quad ~s_is_j = \pm 1$

$e^{Ks_is_j} = e^{-K}(1 + v \delta_{s_i, s_j}), \quad v = e^{2K} - 1,~s_is_j = \pm 1$

$$\mathcal{Z}_{\rm FK} = $$

$$\mathcal{Z}_{\rm Loop} = $$