Magnetic phase diagram of the Hubbard model with next-nearest-neighbour hopping

We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest-neighbour (NN) hopping t(1) and next-nearest-neighbour (NNN) hopping t(2) in the limit of infinite coordination. We use the amplitude t(2)/t(1) of the NNN hopping to tune the density of states (DOS) of the non-interacting system from a situation with particle-hole symmetry to an asymmetric one with van-Hove singularities at the lower (t(2)/t(1)>0) respectively upper (t(2)/t(1)<0) band edge for large enough |t(2)/t(1)|. For this strongly asymmetric situation, we find rather extended parameter regions with ferromagnetic states and regions with antiferromagnetic states.