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.