====== XY模型 ======
$$
{s_i^x}^2+{s_i^y}^2=1
$$

$$
{\cal H}=\displaystyle\sum_{\langle i,j\rangle}J_{ij}\left(s_i^x s_j^x+s_i^y s_j^y\right)
$$

$$
\vec{s}_i=\left(s_i^x, s_i^y\right)
$$

$$
\left|\vec{s}_i\right|=1
$$


$$
{\cal H}=\displaystyle\sum_{\langle i,j\rangle}J_{ij}\vec{s}_i\cdot\vec{s}_j
$$

$$
{\cal H}=\displaystyle\sum_{\langle i,j\rangle}J_{ij}cos\left(\varphi_i-\varphi_j\right)
$$


===== Li/Cu(001) =====