Dimensional Crossover In The Aging Dynamics Of Spin Glasses In A Film Geometry

Motivated by recent experiments of exceptional accuracy, we study numerically the spin-glass dynamics in a film geometry. We cover all the relevant time regimes, from picoseconds to equilibrium, at temperatures at and below the 3D critical point. The dimensional crossover from 3D to 2D dynamics, which starts when the correlation length becomes comparable to the film thickness, consists of four dynamical regimes. Our analysis, based on a renormalization group transformation, finds consistent the overall physical picture employed by Orbach and co-workers in the interpretation of their experiments.