Monte Carlo study of order–disorder layering transitions in the Blume–Capel model

The order–disorder layering transitions, of the spin-1 Blume–Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. The system exhibits tri-critical behavior and reentrant phenomena. The reentrant phenomena is found for the first k0 layers from the surface, where k0 is exactly the number of layering transitions at the ground state. This is qualitatively in agreement with mean field results. Layer magnetizations, quadrupolar and magnetic susceptibilities are calculated. The critical exponents of magnetic susceptibility of each layer are computed for N=10 and different sizes of the system. It is found that the critical exponent of a 2D layer in a film is different than the one of a free 2D layer. Indeed the critical exponent of a layer depends strongly on its position from the surface.