Further results on the critical behaviour of the mean spherical model: layer and local susceptibilities

The critical behaviour of some properties of the ferromagnetic mean spherical model with a film geometry L×∞2 and the Neumann–Dirichlet boundary conditions is investigated in the presence of three external fields: a bulk field, a step-like (+−) field which changes sign at distance Lx(0⩽x⩽1) from the Neumann boundary and a surface field acting on the lth layer. The behaviour of the mean spherical constraint is studied at three different temperatures and field regimes: high-temperature bulk limit, critical finite-size scaling regime, and low-temperature moderate-field regime. Exact expressions for the layer and local susceptibilities are derived and studied in the three different regimes.