Surface and thin film magnetization of isotropic and anisotropic Heisenberg ferromagnet at low temperatures

The independent random walk method (which is equivalent to the noninteracting spin wave method) with no further approximations was used to calculate the low temperature expansion of: (i) the local mean spin values of an isotropic Heisenberg ferromagnet for semi-infinite crystal and (ii) the spontaneous magnetization of an anisotropic Heisenberg ferromagnet for monolayer and double layer. The full low temperature expansion starting with T-3/2 term was obtained for the semi-infinite Heisenberg ferromagnet and it was shown that the spontaneous magnetization for thin films of anisotropic Heisenberg ferromagnets can exhibit a quasi-linear behaviour in certain temperature region related to the magnitude of the anisotropy.