XYchain with random anisotropy: Magnetization law, susceptibility, and correlation functions atT=0

The random-anisotropy model in one dimension, at zero temperature, is studied analytically and in Monte Carlo simulations, focusing on the magnetization curve as a function of disorder strength D, and on the susceptibility and correlation functions. The predicted scaling of the susceptibility (for weak disorder), χ∝${\mathit{D}}^{\mathrm{-}4/3}$, is verified, as is the prediction ‖M-1‖∝${\mathit{H}}^{\mathrm{-}3/2}$ on approaching saturation. The correlation length does not follow the expected behavior, ${\mathit{R}}_{\mathit{f}}$∝${\mathit{D}}^{\mathrm{-}2/3}$. Nonequilibrium effects are evident: Hysteresis persists even for small disorder, and (steady-state) correlation functions depend strongly upon the initial state of the system. A new simulation method is introduced, which is more effective than the usual Metropolis algorithm for weak disorder.