Mean Field Study of Size Scaling in Ising Thin Films

The phase transitions taking place in Ising thin films are studied within the Bragg-Williams and Bethe approximations. The Curie temperature Tc is calculated as a function of the number of layers N for various crystal structures and surface orientations and the scaling relation Δτ = 1 − Tc(N)/Tc(∞) = AN−λ is obtained. It is found that the coefficient A depends on the approximation used and on ratio between the surface and bulk coordination numbers. On the other hand, as expected, for very thick films the exponent λ is the same in both approximations and corresponds to the mean field value.