Curie Temperature of Anisotropic Ferromagnetic Films

Dimensional crossover of ordering in ferromagnetic films with both periodic and free boundary conditions is studied for the exactly solvable uniaxial model of classical D-component spin vectors in the limit D \to \infty. Analytical and numerical solution of the exact equations describing this model shows that for lattice dimensionalities d>4, finite-size corrections to the bulk values of T_c are characterized by the mean-field exponents and anisotropy-dependent amplitudes. For d =< 4, the mean-field behavior is only realized in the region \kappa_c N >> 1, where \kappa_c is the dimensionlesss inverse transverse (with respect to the easy axis) bulk correlation length at T_c and N is the number of layers in the film. In the region \kappa_c N << 1 and the dimensionality range 3 < d =< 4, finite-size corrections are described by the universality class of the isotropic D=\infty model. For d =< 3, magnetic ordering vanishes in the isotropic limit, \kappa_c \to 0, since the film behaves as an object of dimensionality d'=d-1 =< 2 and long-wavelength fluctuations destroy the order. Here the suppression of T_c of a film can be substantial, depending on the competition between the weakening anisotropy and the increasing film thickness. For thick films, T_c becomes small only for very small anisotropy.