Dimensional crossover in dipolar magnetic layers
M. Bulenda, Uwe Claus Täuber, Franz Schwabl
We investigate the static critical behaviour of a uniaxial magnetic layer, with finite thickness L in one direction, yet infinitely extended in the remaining d dimensions. The magnetic dipole-dipole interaction is taken into account. We apply a variant of Wilson's momentum shell renormalization group approach to describe the crossover between the critical behaviour of the 3D Ising, 2D Ising, 3D uniaxial dipolar, and the 2D uniaxial dipolar universality 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 with varying upper critical dimensions. While the limiting cases can be discussed by means of dimensional expansions with respect to the appropriate upper critical dimensions, respectively, the crossover features must be addressed in terms of the renormalization group flow trajectories at fixed dimensionality d .
arXiv:cond-mat/9907029•Journal of Physics A Mathematical and General•Dec 15, 1999•32 citations