Stability Analysis of the Hubbard-Model

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An effective Hartree-Fock-Bogoliubov-type interaction is calculated for the Hubbard-model in second order in the coupling by means of flow-equations. A stability analysis is performed in order to obtain the transition into various possible phases. We find, that the second order contribution weakens the tendency for the antiferromagnetic transition. Apart from a possible antiferromagnetic transition the d-wave Pomeranchuk instability recently reported by Halboth and Metzner is usually the strongest instability. A newly found instability is of p-wave character and yields a band-splitting. In the BCS-channel one obtains the strongest contribution for dₓ₂₋y₂-waves. Other types of instabilities of comparable strength are also reported.