Study of the confined Ising magnet with long-range competing boundary fields

Abstract

We present extensive Monte Carlo simulations of the Ising film confined in anL × M geometry () in the presence of long-range competing magnetic fieldsh(n) = h1/n3(n = 1,2,...,L) which are applied at opposite walls along theM-direction. Due to the fields, an interface between domains of different orientations thatruns parallel to the walls forms and can be located close to one of the two surfaces orfluctuate in the centre of the film (localization–delocalization transition). This transition isthe precursor of the wetting phase transition that occurs in the limit of infinite filmthickness () at the critical curve Tw(h1). For T<Tw(h1) (T≥Tw(h1)) such an interface is bound to (unbound from) the walls.We study this transition by measuring the magnetization profiles across thesample and the distribution function of both the magnetization of the wholesample and that of the centre of the film as a function of temperature,T, or strength ofthe wall field, h1. We obtain estimates of the size-dependent wetting ‘critical’ points that allow us toextrapolate to the thermodynamic limit. Using the results of these extrapolations,confirmed by independent measurements of the cumulant, we draw the phase diagram ofthe wetting transition with long-range surface fields.We show that, starting from a localized interface well inside the non-wet phase, theposition of the interface diverges exponentially when approaching the transition point, incontrast to the power-law divergence observed in the case of short-range fields.The properties of the delocalized interface are also studied. Within the wet phase the widthof the capillary waves broadens the observed interface profiles. The spectrum of capillarywaves is cut off at large wavelengths by the correlation length, , which scales like , similar to the short-range case. Additionally, the interface stiffness is obtained from theFourier spectrum of the capillary waves.