Surface critical behavior and scaling functions for the three-dimensional mean spherical model

The d-dimensional mean spherical model on a fully finite Ld simple cubic lattice with Neumann-Dirichlet boundary conditions is considered in the presence of a surface external fields acting at the surfaces bounding the system. Exact calculations are evaluated for the fully finite system and in the case of a film geometry L×∞d−1. Critical finite-size scaling functions both for the specific heat and the mean-square magnetization are derived and investigated close to and below the bulk critical temperature Kc.