On the finite-size behaviour of systems with asymptotically large critical shift

Exact results of the finite-size behaviour of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature Tc are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent λ characterizing the shift of the finite-size critical temperature with respect to Tc is smaller than 1/ν, with ν being the critical exponent of the bulk correlation length