The antiferromagnetic Ising chain in a mixed transverse and longitudinal magnetic field

We have studied the antiferromagnetic Ising chain in a transverse magnetic field $h_{x}$ and uniform longitudinal field $h_{z}$. Using the density matrix renormalization group calculation combined with a finite-size scaling the ground state phase diagram in ($h_{x},h_{z}$) plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in $h_{z}$ the scaling behavior of the mass gap in the vicinity of the critical point ($h_{x}=1/2,h_{z}=0$) is established. It is found that the form of the transition line near the classical multicritical point ($h_{x}=0,h_{z}=1$) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.