Eur. Phys. J. B (2014) 87: 303
https://doi.org/10.1140/epjb/e2014-50336-5

Regular Article

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

¹ Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CCT La Plata. CONICET, UNLP. Calle 59, No. 789, 1900 La Plata, Argentina
² Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina
³ Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina

^a e-mail: ezequielalb@yahoo.com.ar

Received: 25 May 2014
Received in final form: 28 October 2014
Published online: 15 December 2014

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), H₁(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[-3.4mm] value (H_eff ≡ ¹/_λ ƒ₀ ^λH₁(x,λ)dx > 0) 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 δH_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 δH_max, respectively. On the other hand, for H₁(x,λ) ≠ 0 but H_eff = 0 bulk standard critical behavior results is observed.