On the decoupling effects in the spherical model

Abstract

The decoupling effects in the ferromagnetic mean spherical model with a layer geometry of finite thickness L, under Dirichlet boundary conditions, and in the presence of a step-like (+−) external field, are reconsidered. The result of Abraham and Robert, that in the bulk limit the magnetization profile near the Dirichlet boundary is exactly the same as the one near the central layer of zero magnetization has a possible interpretation within the following decoupling hypothesis. Dirichlet (respectively, Neumann) boundary conditions can be thought of being physically realizable, at least in the spherical model, by coupling together two identical copies of the system placed in uniform fields of equal magnitude and opposite (respectively, the same) sign. We show that this is indeed the case as far as the magnetization profile is considered on the scale of a large bulk correlation length, in the high-temperature bulk limit close to the critical point. The decoupling effects in the magnetization profile are studied also in the critical finite-size scaling regime and in the low-temperature moderate-field regime. In general, it is found that the decoupling hypothesis breaks down since the mean square length of the spins at the Dirichlet (Neumann) boundary is different from the one at the central layers of a system in a step-like (uniform) field.