  We investigate a two-dimensional Ising model with long-range interactions
that emerge from a generalization of the magnetic dipolar interaction in spin
systems with in-plane spin orientation. This interaction is, in general,
anisotropic whereby in the present work we focus on the isotropic case for
which the model is found to be at its upper critical dimensionality. To
investigate the critical behavior the temperature and field dependence of
several quantities are studied by means of Monte Carlo simulations. On the
basis of the Privman-Fisher hypothesis and results of the renormalization group
the numerical data are analyzed in the framework of a finite-size scaling
analysis and compared to finite-size scaling functions derived from a
Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The
obtained excellent agreement suggests that at least in the present case the
concept of universal finite-size scaling functions can be extended to the upper
critical dimensionality.

Statistical Mechanics