Surface magnetism: A Monte Carlo study of surface critical behavior

We study the critical behavior of an Ising model on a simple cubic lattice with two free surfaces using the Monte Carlo method. The effect of both the ratio of surface to bulk coupling Jₛ/Jb, and the length to width ratio, r=L/D, are considered. The spontaneous magnetization and the magnetic susceptibility near the critical point are calculated for both the surface and the bulk. For sufficiently large ratio Jₛ/Jb, we find that the surface magnetizes at a higher temperature than the bulk, as has been reported previously. However, we find that the critical value of Jₛ/Jb, where the surface and bulk magnetization vanish at the same temperature, depends on the aspect ratio r, and that for a range of values of r this can be less than the value 1.55 valid for a semi-infinite geometry. The results reported here may be applicable to thin magnetic films.