| The key influence of boundary conditions on the Casimir force has long been recognized. In the case of the critical Casimir force, the experiments of Garcia, Chan and co-workers highlight the importance of boundary conditions; the Dirichlet boundary conditions that apply to the superfluid order parameter in 4He result in a critical Casimir force that is substantially larger immediately below the superfluid transition temperature than it would be if boundary conditions were periodic. In an attempt to elucidate the interplay of boundary conditions and dimensionality in the determination of the critical Casimir force, we have investigated the critical Casimir force in the exactly solvable cases of the Ising model in one and two dimensions. Additionally, a preliminary attempt has been made to determine the critical Casimir force for the Ising model in four dimensions, where the bulk is described by an field theory with vanishing fourth order coupling, while the investigation of the behavior of the three dimensional "film" requires the utilization of numerical methods. |
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