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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 $δ$. The latter generates a magnetization plateau at $M=(1-q/π)/2$, which evolves with strength $δ$ of the perturbation as $δ^ε$, where $ε=ε(h_{3},α)$ 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.