Excess free energy and Casimir forces in systems with long-range interactions of van der Waals type: general considerations and exact spherical-model results.

We consider systems confined to a d-dimensional slab of macroscopic lateral extension and finite thickness L that undergo a continuous bulk phase transition in the limit L --> infinity and are describable by an O(n) symmetrical Hamiltonian. Periodic boundary conditions are applied across the slab. We study the effects of long-range pair interactions whose potential decays as bx-(d+sigma) as x --> infinity, with 2