Critical behavior of two-dimensional magnetic systems with dipole-dipole interactions

The critical exponents of two-dimensional dipolar magnetic systems with isotropic in-plane ordering may be obtained from the $\epsilon$ expansion which determines the exponents of isotropic three-dimensional dipolar systems. However, a two-dimensional dipolar system with uniaxial in-plane ordering requires a new $\epsilon$ expansion with upper critical dimension $d_c=3\mathrm{}\frac{1}{2}$. The possible relevance to experimental studies of monolayers of gadolinium is briefly discussed.