Corner wetting in the two-dimensional Ising model: Monte Carlo results

E. V. ALBANO; A. DE VIRGILIIS; M. MUELLER; K. BINDER

JOURNAL OF PHYSICS CONDENSED MATTER

Institue of Physics (UK)

Año: 2003 vol. 15 p. 333 - 345

0953-8984

Square L × L (L = 24–128) Ising lattices with nearest neighbour ferromagnetic exchange are considered using free boundary conditions at which boundary magnetic fields &pm; h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field −h acts. For temperatures T less than the critical temperature Tc of the bulk, this boundary condition leads to the formation of two domains with opposite orientations of the magnetization direction, separated by an interface which for T larger than the filling transition temperature Tf (h) runs from the upper left corner to the lower right corner, while for T < Tf (h) this interface is localized either close to the lower left corner or close to the upper right corner. Numerous theoretical predictions for the critical behaviour of this ´corner wetting´ or ´wedge filling´ transition are tested by Monte Carlo simulations. In particular, it is shown that for T = Tf (h) the magnetization profile m(z) in the z-direction normal to the interface is simply linear and the interfacial width scales as w L, while for T > Tf (h) it scales as w √ L. The distribution P () of the interface position (measured along the z-direction from the corners) decays exponentially for T < Tf (h) from either corner, is essentially flat for T = Tf (h) and is a Gaussian centred at the middle of the diagonal for T > Tf (h). Furthermore, the Monte Carlo data are compatible with (Tf (h) − T)−1 and a finite size scaling of the total magnetization according to M(L, T) = {(1 − T/Tf (h))ν L} with ν = 1. Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.