Novel correlations in two dimensions: Some exact solutions
  We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring. 
M. V. N. Murthy, R. K. Bhaduri and Diptiman Sen (Department of Physics   and Astronomy, McMaster University, Hamilton, Ontar...