6533b870fe1ef96bd12d058e

RESEARCH PRODUCT

Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields

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Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ Ising lattices with nearest neighbor ferromagnetic exchange and four free $L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ surfaces, at which antisymmetric surface fields $\ifmmode\pm\else\textpm\fi{}{H}_{s}$ act, are studied for a wide range of linear dimensions $(4l~Ll~320,30l~{L}_{y}l~1000),$ in an attempt to clarify finite size effects on the wedge filling transition in this ``double-wedge'' geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature ${T}_{c}$ this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For ${L,L}_{y}\ensuremath{\rightarrow}\ensuremath{\infty}$ and T larger than the filling transition temperature ${T}_{f}{(H}_{s}),$ this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For $Tl{T}_{f}{(H}_{s}),$ however, this interface is bound either to the wedge where the two surfaces with field $\ensuremath{-}{H}_{s}$ meet (then the total magnetization m of the system is positive) or to the opposite wedge (then $ml0).$ The distance ${l}_{0}$ of the interface midpoint from the wedges is studied as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{f}{(H}_{s})$ from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of ${l}_{0}$ for $Tg{T}_{f}{(H}_{s})$ as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length ${\ensuremath{\xi}}_{y}$ in the y direction along the wedges is also studied, and we find no transition for finite L and ${L}_{y}\ensuremath{\rightarrow}\ensuremath{\infty}.$ For $\stackrel{\ensuremath{\rightarrow}}{L}\ensuremath{\infty}$ the prediction ${l}_{0}\ensuremath{\propto}{(H}_{\mathrm{sc}}\ensuremath{-}{H}_{s}{)}^{\ensuremath{-}1/4}$ is verified, where ${H}_{\mathrm{sc}}(T)$ is the inverse function of ${T}_{f}{(H}_{s})$ and ${\ensuremath{\xi}}_{y}\ensuremath{\propto}{(H}_{\mathrm{sc}}\ensuremath{-}{H}_{s}{)}^{\ensuremath{-}3/4},$ respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.