The influence of three external fields on the mean spherical model: magnetization profile

Explicit expressions are derived for the free energy, and the magnetization profile of the three-dimensional mean spherical model with a layer geometry of finite thickness L, under Neumann–Dirichlet boundary conditions in the presence of three external fields: a bulk field, a step-like (±) field, and a surface field acting on the lth layer. The scaling functions that govern the critical behaviour of the system are derived and, with the use of the asymptotic properties of these functions, various predictions of the Privman–Fisher scaling hypothesis are verified in the finite-size scaling regime.