Weakly interacting two-dimensional system of dipoles: limitations of   mean-field theory
  We consider a homogeneous 2D Bose gas with repulsive dipole-dipole interactions. The ground-state equation of state, calculated using the Diffusion Monte Carlo method, shows quantitative differences with predictions of commonly used Gross-Pitaevskii mean-field theory. The static structure factor, pair distribution function and condensate fraction are calculated in a wide range of the gas parameter. Differences with mean-field theory are reflected in the frequency of the lowest ``breathing'' mode for harmonically trapped systems. 
G.E. Astrakharchik, J. Boronat, J. Casulleras, I.L. Kurbakov, Yu.E.   Lozovik