XY chain with random anisotropy: Magnetization law, susceptibility, and correlation functions at T=0.

TLDR: Ce modele d'anisotropie est etudie analytiquement et dans des simulations de Monte Carlo, et se focalise sur the courbe d'aimantation en fonction de l'importance du desordre D, et sur the susceptibilite et les fonctions de correlation.

Abstract: 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), \ensuremath{\chi}\ensuremath{\propto}${\mathit{D}}^{\mathrm{\ensuremath{-}}4/3}$, is verified, as is the prediction \ensuremath{\Vert}M-1\ensuremath{\Vert}\ensuremath{\propto}${\mathit{H}}^{\mathrm{\ensuremath{-}}3/2}$ on approaching saturation. The correlation length does not follow the expected behavior, ${\mathit{R}}_{\mathit{f}}$\ensuremath{\propto}${\mathit{D}}^{\mathrm{\ensuremath{-}}2/3}$. 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.