In this paper, we show how the two-particle Green function (2PGF) can be obtained within the framework of the Dual Fermion approach. This facilitates the calculation of the susceptibility in strongly correlated systems where long-ranged non-local correlations cannot be neglected. We formulate the Bethe-Salpeter equations for the full vertex in the particle-particle and particle-hole channels and introduce an approximation for practical calculations. The scheme is applied to the two-dimensional Hubbard model at half filling. The spin-spin susceptibility is found to strongly increase for the wavevector $vc{q}=(pi,pi)$, indicating the antiferromagnetic instability. We find a suppression of the critical temperature compared to the mean-field result due to the incorporation of the non-local spin-fluctuations.
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