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\begin{document}

\begin{eqnarray*}
 U &=&  \frac{1}{2} K (|\rho_{\vec{k}}| - a)^2 \\
 \rho_{\vec{k}} &=& \sum_j^N \exp(-i\vec{k} \cdot \vec{r}_j )/\sqrt{N} \\
 \vec{k} &=& (2\pi n_x /L_x , 2\pi n_y  /L_y , 2\pi n_z/L_z ) 
\end{eqnarray*}

\end{document}
