NEW SURFACE CRITICAL EXPONENTS IN THE SPHERICAL MODEL

The three-dimensional mean spherical model with a L-layer film geometr y, under Neumann-Neumann and Neumann-Dirichlet boundary conditions is considered. Surafce fields h(1) and h(L). are supposed to act at the s urfaces bounding the system. In the case of Neumann boundary condition s a new surface critical exponent Delta(1)(sb) = 3/2 is found. It is a rgued that this exponent corresponds to a special (surface-bulk) phase transition in the model. The Privman-Fisher scaling hypothesis for th e 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 fr om the Dirichlet boundary, a family of critical exponents emerges: the ir values depend on the exponent defining how the distance scales with the finite size of the system, and interpolate continuously between t he extreme cases Delta(1)(o) = 1/2 and Delta(1)(sb) = 3/2.