We have studied the antiferromagnetic Ising chain in a transverse magnetic field hx and uniform longitudinal field hz. Using the density matrix renormalization group calculation combined with a finite-size scaling the ground state phase diagram in (hx, hz) 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 hz the scaling behavior of the mass gap in the vicinity of the critical point (hx = 1/2, hz = 0) is established. It is found that the form of the transition line near the classical multicritical point (hx = 0, hz = 1) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.

The ground state phase diagram of the 1D XXZ model in a transverse magnetic field is obtained. It consists of the gapped phases with different types of long range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of critical lines. 75.10.Jm -Quantized spin modelsThe study of the 1D spin-1/2 XXZ model in a transverse magnetic field has been drawn much attention last years. The Hamiltonian of this model is:The spectrum of the XXZ model for −1 < ∆ ≤ 1 is gapless. When the transverse magnetic field is applied a gap in the excitation spectrum seems to open up. It is supposed [1] that this effect can explain the peculiarity of low temperature specific heat in Y b 4 As 3 [2]. The magnetic properties of this compound is described by the XXZ Hamiltonian with ∆ ≈ 0.98 and it was shown [1] that the magnetic field in an easy plain induces a gap in the spectrum leading to a dramatic decrease of the linear term in the specific heat.At h = 0 the model (1) is the well-known XXZ model. In the Ising-like region ∆ > 1 the ground state of the XXZ model has the Neel long-range order (LRO) along the Z axis and there is a gap in excitation spectrum. In the region −1 < ∆ ≤ 1 system is in the so-called spin-liquid phase with a power-low decay of correlations. Finally, for ∆ < −1 the ground state is the classical ferromagnet with the gap above the ferromagnetic state.At h = 0 the total S z is not conserving and the model (1) is not integrable, except some special cases: ∆ = 1 and ∆ → ±∞. In addition, there is a 'classical' line h cl (∆) = 2(1 + ∆), where the quantum fluctuations of XXZ model are compensated by the transverse field and the exact ground state of (1) is a classical one [3]. The excited states on the classical line are generally unknown (except some of them [4]), though it is assumed that the spectrum is gapped.In the limits ∆ → ±∞ the model (1) reduces to the 1D Ising model in the transverse field (ITF), for which the phase transition occurs at h c = |∆|/2. At this field the gap is closed and the LRO in Z direction vanishes.It was shown [5] that the phase transition of this type takes place for any ∆ > 0. One can expect also that such a transition exists for any finite ∆ at some critical value h = h c (∆) and there is the transition line connecting two limiting points ∆ → ±∞. Besides, there are other transition lines characterizing by vanishing of both the gap and the LRO. These lines are: h = 0, |∆| < 1; ∆ = 1, h < 2; ∆ = −1, h < h c (−1). However, the critical properties in the vicinity of these transition lines are not known yet.Thus, we expect that the phase diagram of the model (1) (on (∆, h) plane) has a form shown on Fig.1. It contains four regions corresponding to different phases and separated by the transition lines at which the gap vanishes. Each phase is characterized by its own type of the LRO: the Neel order along the Z axis in the region (1); the f...

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One dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces the gap in the spectrum of the model with easy-plain anisotropy. Using conformal invariance the field dependence of the gap at small fields is found. The ground state phase diagram is obtained. It contains four phases with different types of the long range order (LRO) and a disordered one. These phases are separated by critical lines, where the gap and the long range order vanish. Using scaling estimations and a mean-field approach as well as numerical calculations in the vicinity of all critical lines we found the critical exponents of the gap and the LRO. It is shown that transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model. 75.10.Jm -Quantized spin models