NEW EFFECTS IN THE MAGNETIZATION PROFILE OF THE SPHERICAL MODEL IN A STEP-LIKE FIELD

The ferromagnetic mean spherical model, with a layer geometry of thick ness L and Neumann-Dirichlet boundary conditions is investigated in th e presence of a step-like (+-) external field which changes sign at di stance Lx (0 less than or equal to x less than or equal to 1) from the Neumann boundary. The amplitude of the held can be taken to vanish in the thermodynamic limit as an inverse power of L. Exact expressions f or the magnetization profile are derived and studied in three differen t 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 ex ist two special values of x, denoted by x(1,2), 0 < x(1) < x(2) < 1, w hich depend on the scaled temperature and field variables, and have th e property that the magnetization changes sign only when x(1) < x < x( 2). The magnetization is everywhere negative when 0 less than or equal to x < x(1) and everywhere positive when x(2) < x less than or equal to 1. In the low-temperature moderate-field regime we establish that t he field-induced critical point, in the case of periodic boundary cond itions and a step-like field with x = 1/2, appears at x = 1/3.