New effects in the magnetization profile of the spherical model in a step-like field

Abstract

The ferromagnetic mean spherical model with a layer geometry of thickness L and Neumann-Dirichlet boundary conditions is investigated in the presence of a step-like external field which changes sign at distance from the Neumann boundary. The amplitude of the field can be taken to vanish in the thermodynamic limit as an inverse power of L. Exact expressions for the magnetization profile are derived and studied in three different temperature and field regimes: high-temperature bulk limit, critical finite-size scaling regime, and low-temperature moderate-field regime. It is found that in the critical finite-size scaling regime there exist two special values of x, denoted by , , which depend on the scaled temperature and field variables, and have the property that the magnetization changes sign only when . The magnetization is everywhere negative when and everywhere positive when . In the low-temperature moderate-field regime we establish that the field-induced critical point, in the case of periodic boundary conditions and a step-like field with , appears at .