We investigate ground-state energies and magnetization curves in the one-dimensional XXZ model with next-to-nearest neighbor coupling ␣Ͼ0 and anisotropy ⌬ (Ϫ1р⌬р1) at Tϭ0. In between the familiar ferro-and antiferromagnetic phase we find a transition region-called the metamagnetic phase-where the magnetization curve is discontinuous at a critical field B c (␣,⌬). ͓S0163-1829͑98͒01718-4͔

In the presence of a uniform field the one-dimensional spin-1 2 antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.

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We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field h3 and a dimer field with period q and strength δ. The latter generates a magnetization plateau at M = (1 − q/π)/2, which evolves with strength δ of the perturbation as δ ǫ , where ǫ = ǫ(h3, α) is related to the η-exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched of (δ = 0). We also discuss the appearance of magnetization plateaus in ladder systems with l legs.

We investigate the critical exponents η3(α, M ), η1(α, M ) associated with the singularities in the longitudinal and transverse structure factors of the one dimensional antiferromagnetic Heisenberg model with nearest (J1) and next to nearest (J2) neighbour coupling of relative strength α = J 2 J 1 and an external field B with magnetization M (B).