Critical wetting in the two-dimensional Ising ferromagnet confined between inhomogeneous walls

Abstract

We present a numerical study of the critical wetting behavior of an Ising magnet confined between two walls, separated by a distance L, where short-range inhomogeneous surface magnetic fields act. So, samples are assumed to have a size L × M, L being the width and M the length, respectively. By considering surface fields varying spatially with a given wavelength or period (λ), H 1(x,λ) with 1 ≤ x ≤ M, we found that the wetting temperature is given by the exact result of Abraham [D.B. Abraham, Phys. Rev. Lett. 44, 1165 (1980)] provided that an effective field given by the spacial average value $$\left( {H_{eff} \equiv \tfrac{1} {\lambda }\int_0^\lambda {H_1 (x,\lambda )dx > 0} } \right)$$ is considered. The above results hold in the low wavelength regime, while for λ → ∞ and a bivaluated surface field (i.e., H max for x ≤ M/ 2, and δ H max for x>M/ 2, with 0 <δ< 1), one observes two almost independent wetting transitions, both being compatible with Abraham’s exact results corresponding to H max and δ H max, respectively. On the other hand, for H 1(x,λ) ≠ 0 but H eff = 0 bulk standard critical behavior results is observed.