Magnetic phase transition at a surface: Mean-field theory

Within mean-field theory, it is possible to analytically calculate the spatial and temperature dependence of the magnetization near a surface and near a phase transition. These algebraic forms are then used in the Landau-Ginzburg free energy to obtain the surface specific heat and a relaxation time for the surface spins driven to a weak nonequilibrium. These physical quantities have been found to have a temperature dependence that varies continuously with the change in the surface-plane exchange constant. Such a behavior is interpreted in terms of an interplay between the correlation length ξ and the extrapolation length λ where λ effectively determines the range of the surface effects.