Abstract
The three-dimensional mean spherical model with a L-layer film geometry, under Neumann - Neumann and Neumann - Dirichlet boundary conditions is considered. Surafce fields and are supposed to act at the surfaces bounding the system. In the case of Neumann boundary conditions a new surface critical exponent is found. It is argued that this exponent corresponds to a special (surface - bulk) phase transition in the model. The Privman - Fisher scaling hypothesis for the free energy is verified and the corresponding scaling functions for both the Neumann - Neumann and Neumann - Dirichlet boundary conditions are explicitly derived. If the layer field is applied at some distance from the Dirichlet boundary, a family of critical exponents emerges: their values depend on the exponent defining how the distance scales with the finite size of the system, and interpolate continuously between the extreme cases and .
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