=-\frac{1}{N}\sum_{\vec{k}}J(\vec{k})\sum_{\vec{k}_1  ,\vec{k}_2}\hat{a}^+_{\vec{k}_1}\hat{a}_{\vec{k}_2  }\langle \hat{a}_{\vec{k}-\vec{k}_1+\vec{k}_2}\hat{a}_{-\vec{k}}\rangle