Stability Analysis of the Hubbard Model

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 band splitting. In the BCS channel one obtains the strongest contribution for ... waves. Other types of instabilities of comparable strength are also reported.