Dimensional crossover in dipolar magnetic layers

We investigate the static critical behaviour of a uniaxial magnetic layer, with finite thickness L in one direction, yet infinitely extended in the re maining d dimensions. The magnetic dipole-dipole interaction is taken into account. We apply a variant of Wilson's momentum shell renormalization grou p approach to describe the crossover between the critical behaviour of the 3D Ising, 2D Ising, 3D uniaxial dipolar, and the 2D uniaxial dipolar univer sality classes. The corresponding renormalization group fixed points are in addition to different effective dimensionalities characterized by distinct analytic structures of the propagator, and are consequently associated wit h varying upper critical dimensions. While the limiting cases can be discus sed by means of dimensional epsilon expansions with respect to the appropri ate upper critical dimensions, respectively, the crossover features must be addressed in terms of the renormalization group flow trajectories at fixed dimensionality d.