Thin Ising films with competing walls: A Monte Carlo study.

Abstract

Ising magnets with a nearest neighbor ferromagnetic exchange interaction J on a simple cubic lattice are studied in a thin film geometry using extensive Monte Carlo simulations. The system has two large L\ifmmode\times\else\texttimes\fi{}L parallel free surfaces, a distance D apart from each other, at which competing surface fields act, i.e., ${\mathit{H}}_{\mathit{D}}$=-${\mathit{H}}_{1}$. In this geometry, the phase transition occurring in the bulk at a temperature ${\mathit{T}}_{\mathit{c}\mathit{b}}$ is suppressed, and instead one observes the gradual formation of an interface between coexisting phases stabilized by the surface fields. While this interface is located in the center of the film for temperatures ${\mathit{T}}_{\mathit{c}}$(D)T\ensuremath{\lesssim}${\mathit{T}}_{\mathit{c}\mathit{b}}$, and the average order parameter of the film is hence zero, at ${\mathit{T}}_{\mathit{c}}$(D) we observe the interface localization-delocalization transition predicted by Parry and Evans [Phys. Rev. Lett. 64, 439 (1990); Physica A 181, 250 (1992)]. For T${\mathit{T}}_{\mathit{c}}$(D), there is thus a symmetry breaking, and the interface is located either close to the left wall where ${\mathit{H}}_{1}$0 (and the total film magnetization is then positive) or close to the right wall where ${\mathit{H}}_{\mathit{D}}$=-${\mathit{H}}_{1}$g0 (and the total magnetization is negative). As predicted, for large D this transition temperature ${\mathit{T}}_{\mathit{c}}$(D) is close to the wetting transition ${\mathit{T}}_{\mathit{w}}$(${\mathit{H}}_{1}$) of the semi-infinite system, but the transition nevertheless has a two-dimensional Ising character. Due to crossover problems (for D\ensuremath{\rightarrow}\ensuremath{\infty} the width of the asymptotic Ising region shrinks to zero, and one presumably observes critical wetting in this model) this Ising nature is clearly seen only for rather thin films. For ${\mathit{T}}_{\mathit{c}}$(D)T${\mathit{T}}_{\mathit{c}\mathit{b}}$ evidence for a correlation length ${\ensuremath{\xi}}_{\mathrm{\ensuremath{\parallel}}}$ that varies exponentially with film thickness is obtained and compared to corresponding theoretical predictions.