  We consider a modified version of the one-dimensional Hubbard model, the
t1-t2 Hubbard chain, which includes an additional next-nearest-neighbor
hopping. It has been shown that at weak coupling this model has a Luttinger
liquid phase or a spin liquid phase depending upon the ratio of t2 to t1.
Additionally if the on-site interaction U is large enough, the ground state is
fully polarized. Using exact diagonalization and the density-matrix
renormalization group, we show that the transition to the ferromagnetic phase
is either of first or second order depending on whether the Luttinger liquid or
spin liquid is being destabilized. Since we work at T=0, the second order
transition is a quantum magnetic critical point.
