Soft modes, Gaps and Magnetization Plateaus in 1D Spin-1/2 Antiferromagnetic Heisenberg Models

We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field $h_{3}$ and a dimer field with period $q$ and strength $\delta$. The latter generates a magnetization plateau at $M=(1-q/\pi)/2$, which evolves with strength $\delta$ of the perturbation as $\delta^{\epsilon}$, where $\epsilon=\epsilon(h_{3},\alpha)$ is related to the $\eta$-exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched of ($\delta=0$). We also discuss the appearance of magnetization plateaus in ladder systems with $l$ legs.