1998/06/16 by D. A. Garanin, Garanin, D. A.
Materials Science · Physics and Astronomy · #Magnetic Properties and Applications #Magnetic properties of thin films #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9806198
11 PR pages, 7 figures, submitted to PRB
arxiv created 1998/06/16 · arxiv updated 2009/11/30
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 → ∞. 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 Tc are characterized by the mean-field exponents and anisotropy-dependent amplitudes. For d =< 4, the mean-field behavior is only realized in the region κc N >> 1, where κc is the dimensionlesss inverse transverse (with respect to the easy axis) bulk correlation length at Tc and N is the number of layers in the film. In the region κc N << 1 and the dimensionality range 3 < d =< 4, finite-size corrections are described by the universality class of the isotropic D=∞ model. For d =< 3, magnetic ordering vanishes in the isotropic limit, κc → 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 Tc of a film can be substantial, depending on the competition between the weakening anisotropy and the increasing film thickness. For thick films, Tc becomes small only for very small anisotropy.