Study of the dynamical approach to the interface localization-delocalization transition of the confined Ising model

Confined magnetic Ising films in a L x D geometry (L << D), with short-range competing magnetic fields (h) acting at opposite walls along the D-direction, exhibit a slightly rounded localization-delocalization transition of the interface between domains of different orientations that runs parallel to the walls. This transition is the precursor of a wetting transition that occurs in the limit of infinite film thickness (L → ∞) at the critical curve Tw(h). For TTw(h)) such an interface is bounded (unbounded) to the walls, while right at Tw(h) the interface is freely fluctuating around the centre of the film. Starting from disordered configurations, corresponding to T → ∞, we quench to the wetting critical temperature and study the dynamics of the approach to the stationary regime by means of extensive Monte Carlo simulations. It is found that for all layers parallel to the wall (rows), the row magnetizations exhibit a peak at a time τmax ∝ L2 and subsequently relax to the stationary, equilibrium behaviour. The characteristic time for such a relaxation scales as τR ∝ L4, as expected from theoretical arguments, that are discussed in detail