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

Abstract

Abstract The d-dimensional mean spherical model on a fully finite L d 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 K c .