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.