Finite size scaling in Ising thin films

The Curie temperature of Ising thin films with various crystalline structures and surface orientations is calculated within the Bragg-Williams and the Bethe approximations. Tc is calculated as a function of the number of layers N and the scaling relation Δτ = 1 - Tc(N)Tc(∞) = AN−λ is obtained. It is analyzed in detail how the coefficient A and the exponent λ depend on the approximation used, on the crystalline structure, on the ratio between the surface and bulk coordination numbers, and how they tend to the asymptotic values.