Properties of the Ising magnet confined in a corner geometry

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields image are applied, i.e., at the two boundary rows ending at the lower left corner a field image acts, while at the two boundary rows ending at the upper right corner a field image acts. For temperatures T less than the critical temperature image of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature image runs from the upper left corner to the lower right corner, while for image this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for image the magnetization profile image in the z-direction normal to the interface simply is linear and the interfacial width scales as image, while for image it scales as image. The distribution image of the interface position image (measured along the z-direction from the corners) decays exponentially for image from either corner, is essentially flat for image, and is a Gaussian centered at the middle of the diagonal for image. 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.