The growth of confined magnetic films with ferromagnetic interactions betweennearest-neighbor spins is studied in a stripped $(1+1)-$dimensional rectangulargeometry. Magnetic films are grown irreversibly by adding spins at theboundaries of the growing interface. A competing situation with two oppositeshort range surface magnetic fields of the same magnitude is analyzed. Due tothe antisymmetric condition considered, an interface between domains with spinshaving opposite orientations develops along the growing direction. Suchinterface undergoes a localization-delocalization transition that is identifiedas a quasi-wetting transition, in qualitative agreement with observationsperformed under equilibrium conditions. In addition, the film also exhibits agrowing interface that undergoes morphological transitions in the growth mode.It is shown that, as a consequence of the nonequilibrium nature of theinvestigated model, the subtle interplay between finite-size effects, wetting,and interface growth mechanisms leads to more rich and complex physicalfeatures than in the equilibrium counterpart. Indeed, a phase diagram thatexhibits eight distinct regions is evaluated and discussed. In thethermodynamic limit, the whole ordered phase (which contains the quasi-wettingtransition) collapses, while within the disordered phase, standardextrapolation procedures show that only two regions are present in the phasediagram of the infinite system.
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